The impersonalists try to prove that the varieties in the vision of the empiric philosopher are false. The impersonalist philosophy, vivarta-vāda, generally cites the acceptance of a rope to be a snake as an example of this fact. According to this example, the varieties within our vision are false, just as a rope seen to be a snake is false. The Vaiṣṇavas say, however, that although the idea that the rope is a snake is false, the snake is not false; one has experience of a snake in reality, and therefore he knows that although the representation of the rope as a snake is false or illusory, there is a snake in reality. Similarly, this world, which is full of varieties, is not false; it is a reflection of the reality in the Vaikuṇṭha world, the spiritual world.
(Srimad Bhagavatam------7:15:58------purport).

This verse is specifically stated to defy the Māyāvāda conclusion of oneness without differentiation between the individual soul and the Supersoul. The Māyāvāda conclusion is that the living entity and the Supersoul are one; there is no difference. The Māyāvādīs proclaim that there is no separate existence outside the impersonal Brahman and that the feeling of separation is māyā, or an illusion, by which one considers a rope to be a snake. The rope-and-the-snake argument is generally offered by the Māyāvādī philosophers. Therefore these words, which representvivarta-vāda, are specifically mentioned herein. Actually Paramātmā, the Supersoul, is the Supreme Personality of Godhead, and He is eternally liberated. In other words, the Supreme Personality of Godhead is living within this body along with the individual soul, and this is confirmed in the Vedas. They are likened to two friends sitting on the same tree. Yet Paramātmā is above the illusory energy. The illusory energy is called bahiraṅgā śakti, or external energy, and the living entity is called taṭasthā śakti, or marginal potency. As stated in Bhagavad-gītā, the material energy, represented as earth, water, air, fire, sky, etc., and the spiritual energy, the living entity, are both energies of the Supreme Lord. Even though the energies and the energetic are identical, the living entity, individual soul, being prone to be influenced by the external energy, considers the Supreme Personality of Godhead to be one with himself.
(Srimad Bhagavatam------4:22:38------purport).

Śrīla Bhaktivinoda Ṭhākura explains, “In the Vedanta-sūtra of Śrīla Vyāsadeva it is definitely stated that all cosmic manifestations result from transformations of various energies of the Lord. Śaṅkarācārya, however, not accepting the energy of the Lord, thinks that it is the Lord who is transformed. He has taken many clear statements from the Vedic literature and twisted them to try to prove that if the Lord, or the Absolute Truth, were transformed, His oneness would be disturbed. Thus he has accused Śrīla Vyāsadeva of being mistaken. In developing his philosophy of monism, therefore, he has established vivarta-vāda, or the Māyāvāda theory of illusion.” In the Brahma-sūtra, Second Chapter, the first aphorism is as follows: tad-ananyatvam ārambhaṇa-śabdādibhyaḥ. Commenting on this sūtra in his Śārīraka-bhāṣya, Śaṅkarācārya has introduced the statement vācārambhaṇaṁ vikāro nāmadheyam from the Chāndogya Upaniṣad (6.1.4) to try to prove that acceptance of the transformation of the energy of the Supreme Lord is faulty. He has tried to defy this transformation of energy in a misguided way, which will be explained later. Since his conception of God is impersonal, he does not believe that the entire cosmic manifestation is a transformation of the energies of the Lord, for as soon as one accepts the various energies of the Absolute Truth, one must immediately accept the Absolute Truth to be personal, not impersonal. A person can create many things by the transformation of his energy. For example, a businessman transforms his energy by establishing many big factories or business organizations, yet he remains a person although his energy has been transformed into these many factories or business concerns. The Māyāvādī philosophers do not understand this simple fact. Their tiny brains and poor fund of knowledge cannot afford them sufficient enlightenment to realize that when a man’s energy is transformed, the man himself is not transformed but remains the same person.
(Sri Caitanya Caritamrta-------1:7:121------purport).

The example of misunderstanding a rope to be a snake is mentioned in the Māṇḍūkya Upaniṣad, but it is meant to explain the error of identifying the body with the soul. Since the soul is actually a spiritual particle, as confirmed in the Bhagavad-gītā (mamaivāṁśo jīva-loke), it is due to illusion (vivarta-vāda) that a human being, like an animal, identifies the body with the self. This is a proper example of vivarta, or illusion. The verse atattvato ’nyathā-buddhir vivarta ity udāhṛtaḥ describes such an illusion. To not know actual facts and thus to mistake one thing for another (as, for example, to accept the body as oneself) is called vivarta-vāda. Every conditioned living entity who considers the body to be the soul is deluded by this vivarta-vāda. One can be attacked by this vivarta-vāda philosophy when he forgets the inconceivable power of the omnipotent Personality of Godhead.
(Sri Caitanya Caritamrta-------1:7:122------purport).

How the Supreme Personality of Godhead remains as He is, never changing, is explained in the Īśopaniṣad: pūrṇasya pūrṇam ādāya pūrṇam evāvaśiṣyate [Īśo Invocation]. God is complete. Even if a complete manifestation is taken away from Him, He continues to be complete. The material creation is manifested by the energy of the Lord, but He is still the same person. His form, entourage, qualities and so on never deteriorate. Śrīla Jīva Gosvāmī, in his Paramātma-sandarbha, comments regarding the vivarta-vāda as follows: “Under the spell of vivarta-vāda one imagines the separate entities, namely the cosmic manifestation and the living entities, to be one with Brahman. This is due to complete ignorance regarding the actual fact. The Absolute Truth, or Parabrahman, is always one and always the same. He is completely free from all other conceptions of existence. He is completely free from false ego, for He is the full spiritual identity. It is absolutely impossible for Him to be subjected to ignorance and fall under the spell of a misconception (vivarta-vāda). The Absolute Truth is beyond our conception. One must admit that He has unblemished qualities that He does not share with every living entity. He is never tainted in the slightest degree by the flaws of ordinary living beings. Everyone must therefore understand the Absolute Truth to possess inconceivable potencies.”
(Sri Caitanya Caritamrta-------1:7:122------purport).

The falsity of Śrīpāda Śaṅkarācārya’s explanation of vivarta-vāda and pariṇāma-vāda has been detected by the Vaiṣṇava ācāryas, especially Jīva Gosvāmī, whose opinion is that actually Śaṅkara did not understand the Vedānta-sūtra. In Śaṅkara’s explanation of one sūtra, ānanda-mayo ’bhyāsāt, he has interpreted the affix mayaṭ with such word jugglery that this very explanation proves that he had little knowledge of the Vedānta-sūtra but simply wanted to support his impersonalism through the aphorisms of the Vedānta philosophy. Actually, however, he failed to do so because he could not put forward strong arguments. In this connection, Śrīla Jīva Gosvāmī cites the phrase brahma pucchaṁ pratiṣṭhā (Taittirīya Up. 2.5), which gives Vedic evidence that Brahman is the origin of everything. In explaining this verse, Śrīpāda Śaṅkarācārya interpreted various Sanskrit words in such a way that he implied, according to Jīva Gosvāmī, that Vyāsadeva had very little knowledge of higher logic. Such unscrupulous deviation from the real meaning of the Vedānta-sūtra has created a class of men who by word jugglery try to derive various indirect meanings from the Vedic literatures, especially the Bhagavad-gītā. One of them has even explained that the word kurukṣetra refers to the body. Such interpretations imply, however, that neither Lord Kṛṣṇa nor Vyāsadeva had a proper sense of word usage or etymological adjustment. They lead one to assume that since Lord Kṛṣṇa could not personally sense the meaning of what He was speaking and Vyāsadeva did not know the meaning of what he was writing, Lord Kṛṣṇa left His book to be explained later by the Māyāvādīs. Such interpretations merely prove, however, that their proponents have very little philosophical sense.
(Sri Caitanya Caritamrta-------1:7:127------purport).

When the atheistic philosophers or the Māyāvādīs, being unable to understand the inconceivable energies of the Supreme Personality of Godhead, imagine an impersonal void, their imagination is only the counterpart of materialistic thinking. Within the material world, there is nothing inconceivable. High-thinking philosophers and scientists can tackle the material energy, but not being able to understand the spiritual energy, they can simply imagine an inactive state, such as the impersonal Brahman. This is simply the negative side of material life. By such imperfect knowledge, the Māyāvādī philosophers conclude that the cosmic manifestation is a transformation of the Supreme. Thus they must necessarily also accept the theory of the illusion of the Supreme (vivarta-vāda). However, if we accept the inconceivable potencies of the Lord, we can understand how the Supreme Personality of Godhead can appear within this material world without being touched or contaminated by the three modes of material nature.
(Sri Caitanya Caritamrta-------2:6:171------purport).

The first verse of the Brahma-sūtra is athāto brahma jijñāsā: “We must now inquire into the Absolute Truth.” The second verse immediately answers, janmādy asya yataḥ: “The Absolute Truth is the original source of everything.” Janmādy asya yataḥ does not suggest that the original person has been transformed. Rather, it clearly indicates that He produces this cosmic manifestation through His inconceivable energy. This is also clearly explained in the Bhagavad-gītā (10.8), where Kṛṣṇa says, mattaḥ sarvaṁ pravartate: “From Me, everything emanates.” This is also confirmed in the Taittirīya Upaniṣad (3.1.1): yato vā imāni bhūtāni jāyante. “The Supreme Absolute Truth is that from which everything is born.” Similarly, in the Muṇḍaka Upaniṣad (1.1.7) it is stated, yathorṇa-nābhiḥ sṛjate gṛhṇate ca: “[The Lord creates and destroys the cosmic manifestation] as a spider creates a web and draws it back within itself.” All of these sūtras indicate the transformation of the Lord’s energy. It is not that the Lord undergoes direct transformation, which is called pariṇāma-vāda. However, being very anxious to protect Śrīla Vyāsadeva from criticism, Śaṅkarācārya became a pseudo gentleman and put forward his theory of illusion (vivarta-vāda). Śaṅkarācārya concocted this meaning of pariṇāma-vāda, and by word jugglery he endeavored very hard to establish pariṇāma-vāda as vivarta-vāda.
(Sri Caitanya Caritamrta-------2:6:172------purport).