Understanding "plenary portions or portions of the plenary portions" of the Krsna the Supreme Personality of Godhead and cause of all causes.

Srimad Bhagavatam - "O brāhmaṇas, the incarnations of the Lord are innumerable, like rivulets flowing from inexhaustible sources of water." (ŚB, Canto 1 Ch 3 text 26)

Srila Prabhupada - "The list of incarnations of the Personality of Godhead given herein is not complete. It is only a partial view of all the incarnations. There are many others, such as-

Śrī Hayagrīva, 

Hari, 

Haṁsa, 

Pṛśnigarbha, 

Vibhu, 

Satyasena, 

Vaikuṇṭha, 

Sārvabhauma, 

Viṣvaksena, 

Dharmasetu, 

Sudhāmā, 

Yogeśvara, 

Bṛhadbhānu, 

And others of the bygone ages. 

Śrī Prahlāda Mahārāja said in his prayer- 

“My Lord, You manifest as many incarnations as there are species of life, namely the aquatics, the vegetables, the reptiles, the birds, the beasts, the men, the demigods, etc, just for the maintenance of the faithful and the annihilation of the unfaithful. 

You advent Yourself in this way in accordance with the necessity of the different yugas. In the Kali-yuga You have incarnated garbed as a devotee, this incarnation of the Lord in the Kali-yuga is Lord Caitanya Mahāprabhu. 

There are many other places, both in the Bhāgavatam and in other scriptures, in which the incarnation of the Lord as Śrī Caitanya Mahāprabhu is explicitly mentioned. In the Brahma-saṁhitā also it is said indirectly that although there are many incarnations of the Lord, such as- 

Rāma, 

Nṛsiṁha, 

Varāha, 

Matsya, 

Kūrma 

And many others.

The Lord Himself sometimes incarnates in person. Lord Kṛṣṇa and Lord Śrī Caitanya Mahāprabhu are not, therefore, incarnations, but the original source of all other incarnations.

This will be clearly explained in the next śloka. So, the Lord is the inexhaustible source for innumerable incarnations which are not always mentioned. But such incarnations are distinguished by specific extraordinary feats which are impossible to be performed by any living being (individual jiva-souls). 

That is the general test to identify an incarnation of the Lord, directly and indirectly empowered. Some incarnations mentioned above are almost plenary portions. For instance- 

The Kumāras are empowered with transcendental knowledge. 

Śrī Nārada is empowered with devotional service. 

Mahārāja Pṛthu is an empowered incarnation with executive function. 

The Matsya incarnation is directly a plenary portion.

So, the innumerable incarnations of the Lord are manifested all over the universes constantly, without cessation, as water flows constantly from waterfalls." (ŚB, Canto 1 Ch 3 text 26 Purport)

Srimad Bhagavatam - "All the ṛṣis, Manus, demigods and descendants of Manu, who are especially powerful, are plenary portions or portions of the plenary portions of the Lord. This also includes the Prajāpatis." (SB, Canto 1 Ch 3 text 27)

Srila Prabhupada - "Those who are comparatively less powerful are called vibhūti, and those who are comparatively more powerful are called āveśa incarnations." (SB, Canto 1 Ch 3 text 27 Purport)

Srimad Bhagavatam - "All of the above-mentioned incarnations are either plenary portions or portions of the plenary portions of the Lord, but Lord Śrī Kṛṣṇa is the original Personality of Godhead. All of them appear on planets whenever there is a disturbance created by the atheists. The Lord incarnates to protect the theists." (SB, Canto 1 Ch 3 text 28)

Srila Prabhupāda - "In this particular stanza Lord Śrī Kṛṣṇa, the Personality of Godhead, is distinguished from other incarnations. He is counted amongst the avatāras (incarnations) because out of His causeless mercy the Lord descends from His transcendental abode. Avatāra means “one who descends." All the incarnations of the Lord, including the Lord Himself, descend to the different planets of the material world as also in different species of life to fulfill particular missions. 

Sometimes He comes Himself, and sometimes His different plenary portions or parts of the plenary portions, or His differentiated portions directly or indirectly empowered by Him, descend to this material world to execute certain specific functions. 

Originally the Lord is full of all opulences, all prowess, all fame, all beauty, all knowledge and all renunciation. When they are partly manifested through the plenary portions or parts of the plenary portions, it should be noted that certain manifestations of His different powers are required for those particular functions. 

When in the room small electric bulbs are displayed, it does not mean that the electric powerhouse is limited by the small bulbs. The same powerhouse can supply power to operate large-scale industrial dynamos with greater volts. 

Similarly, the incarnations of the Lord display limited powers because so much power is needed at that particular time. For example, Lord Paraśurāma and Lord Nṛsiṁha displayed unusual opulence by killing the disobedient kṣatriyas twenty-one times and killing the greatly powerful atheist Hiraṇyakaśipu. 

Hiraṇyakaśipu was so powerful that even the demigods in other planets would tremble simply by the unfavorable raising of his eyebrow. 

The demigods in the higher level of material existence many, many times excel the most well-to-do human beings in duration of life, beauty, wealth, paraphernalia and all other respects. 

Still they were afraid of Hiraṇyakaśipu, thus we can simply imagine how powerful Hiraṇyakaśipu was in this material world. 

But even Hiraṇyakaśipu was cut into small pieces by the nails of Lord Nṛsiṁha. This means that anyone materially powerful cannot stand the strength of the Lord’s nails. 

1 - Similarly, Jāmadagnya displayed the Lord’s power to kill all the disobedient kings powerfully situated in their respective states. 

2 - The Lord’s empowered incarnation Nārada and plenary incarnation Varāha, as well as indirectly empowered Lord Buddha, created faith in the mass of people. 

3 - The incarnations of Rāma and Dhanvantari displayed His fame. 

4 - Balarāma, Mohinī and Vāmana exhibited His beauty. 

5 - Dattātreya, Matsya, Kumāra and Kapila exhibited His transcendental knowledge. 

6 - Nara and Nārāyaṇa Ṛṣis exhibited His renunciation. 

So, all the different indirectly or directly empowered incarnations of the Lord manifested different features, but Lord Kṛṣṇa, the primeval Lord, exhibited the complete features of Godhead, and thus it is confirmed that He is the source of all other incarnations. 

And the most extraordinary feature exhibited by Lord Śrī Kṛṣṇa was His internal energetic manifestation of His pastimes with the cowherd girls. 

His pastimes with the gopīs are all displays of transcendental existence, bliss and knowledge, although these are manifested apparently as sex love. 

The specific attraction of His pastimes with the gopīs should never be misunderstood. The Bhāgavatam relates these transcendental pastimes in the Tenth Canto. 

And in order to reach the position to understand the transcendental nature of Lord Kṛṣṇa’s pastimes with the gopīs, the Bhāgavatam promotes the student gradually in nine other cantos.

According to Śrīla Jīva Gosvāmī’s statement, in accordance with authoritative sources, Lord Kṛṣṇa is the source of all other incarnations. It is not that Lord Kṛṣṇa has any source of incarnation.

All the symptoms of the Supreme Truth in full are present in the person of Lord Śrī Kṛṣṇa, and in the Bhagavad-gītā the Lord emphatically declares that there is no truth greater than or equal to Himself (Krsna). 

In this stanza the word svayam is particularly mentioned to confirm that Lord Kṛṣṇa has no other source than Himself. Although in other places the incarnations are described as bhagavān because of their specific functions, nowhere are they declared to be the Supreme Personality. 

In this stanza the word svayam signifies the supremacy as the summum bonum.

The summum bonum Kṛṣṇa is one without a second. He Himself has expanded Himself in various parts, portions and particles as- 

svayaṁ-rūpa, 

svayam-prakāśa, 

tad-ekātmā, 

prābhava, 

vaibhava, 

vilāsa, 

avatāra, 

āveśa, 

jīva-souls (individual marginal living entities)

All provided with innumerable energies just suitable to the respective persons and personalities. Learned scholars in transcendental subjects have carefully analyzed the summum bonum Kṛṣṇa to have sixty-four principal attributes. 

All the expansions or categories of the Lord possess only some percentages of these attributes but Śrī Kṛṣṇa is the possessor of the attributes cent percent. 

And His personal expansions such as svayam-prakāśa and tad-ekātmā, up to the categories of the avatāras who are all viṣṇu-tattva, possess up to ninety-three percent of these transcendental attributes (exactly 93.75% meaning all Visnu/Narayana  expansions have 60 of Krsna's 64 qualities).

Lord Śiva, who is neither avatāra nor āveśa nor in between them, possesses almost eighty-five percent of the attributes (exactly 85.938% meaning Siva has 55 of Krsna's 64 qualities.

Understanding these percentages is just basic mathematics, for example-

1 - Only Kṛṣṇa the Supreme Personality of Godhead and cause of all causes has all 64 qualities all the time (100%)  

2 - What is the percentage of 60 into 64 = 93.75% (Visnu-tattva or Visnu/ Narayana expansions)

3 - What is the percentage of 55 into 64 = 85.938% (Siva-tattva or Lord Siva and his expansions)

4 - What is the percentage of 50 into 64 = 78.125% (Jiva-tattva, marginal living entities or the individual eternal jiva-souls)  

But the eternal individual jīva-souls, or the individual marginal living entities in different statuses of life, possess up to the limit of seventy-eight percent (exactly 78.125% as mathmatically explained above) of the attributes.

In the conditioned state of material existence, the living being (eternal individual jiva-soul) possesses these attributes in very minute quantity, varying in terms of the pious life of the living being. 

The most perfect of living beings is Brahmā (jiva-soul), the supreme administrator of one material universe. He possesses seventy-eight percent (exactly 78.125% which is having 50 of Krsna's 64 qualities) of the attributes in full. 

All other demigods have the same attributes in less quantity, whereas human beings possess the attributes in very minute quantity. 

The standard of perfection for a human being is to develop the attributes up to seventy-eight percent (exactly 78.125%) in full. The living being can never possess attributes like Śiva, Viṣṇu or Lord Kṛṣṇa.

A living beings (eternal individual jiva-souls) can become godly by developing the seventy-eight-percent (exactly 78.125% as explained above) transcendental attributes in fullness, but he can never become a God like Śiva, Viṣṇu or Kṛṣṇa. He can become a Brahmā in due course. 

The godly living beings who are all residents of the planets in the spiritual sky are eternal associates of God in different spiritual planets called Hari-dhāma and Maheśa-dhāma. 

The abode of Lord Kṛṣṇa above all spiritual planets is called Kṛṣṇaloka or Goloka-Vṛndāvana, and the perfected living being (jiva-souls), by developing seventy-eight percent (78.125% as explained above) of the above attributes in full, can enter the planet of Kṛṣṇaloka after leaving the present material body." (Canto 1 Ch 3 text 28 Purport)××=