Are there different sizes of infinity?

by Administrator / 15 Nov 2014 / Published in Articles /

By Shyamasundara Dasa

http://shyamasundaradasa.com/jyotish/resources/articles/non-jyotish_articles/sizes_of_infinity.html

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25 Comments to “ Are there different sizes of infinity?”

amalagaura says :

Nov 15, 2014 at 1:03 pm

Before we entertain mathematics in relation to scripture we should consider the simple alternative.

eka pad means 1 out of 4.

1. Material World
2. Brahmajyoti
3. Vaikuntha
4. Goloka

I think we don’t need complex mathematics here.

There is a place for such complex mathematics though. I would like to refer you to a book by a devotee who does discuss such complex mathematics in relation to Vedic wisdom and material creation.
1. Somayaji says :
  
  Nov 21, 2014 at 9:27 am
  
  The spiritual sky includes, 2, 3, 4 plus Ayodhya Dham and Dvaraka Dham. See Brhad Bhagavatamrta part 2. And all of them are eternal and unlimited.
2. Nandini dd says :
  
  Nov 24, 2014 at 1:27 pm
  
  Hari bol Prabhu, Don’t mind my saying this but I think you have misapprehended the whole point of this article. No one is questioning that it is one part out of four. In fact it is because it is one out of four that it creating the puzzle because the parts are each infinite. If it had been something finite it would have been easy to grasp. But how you can have 1/4 of infinity?
  
  Shyamasundara Prabhu answered the question in a very elegant way that had been puzzling me for a long time. I was asked the same question by a person I was reaching to “how the material creation is one fourth of spiritual creation when the later is infinite?” I told them I would check with a senior devotee but no one I asked could answer the question in a way that I felt I could bring back to the person who asked. No one, that is, until I read this beautiful answer.
Kulapavana says :

Nov 17, 2014 at 2:03 pm

Perhaps speaking of the ‘size’ of something which is infinite is counter intuitive. Yet, for example, when given a choice between being able to go in 3 directions, or going just in 1 direction, we perceive the second option as more limiting. And indeed, it is more limiting in every sense. So the material world is indeed smaller, or more limiting, then the spiritual world, and we can feel that limiting factor quite easily..
Patitapavana says :

Nov 17, 2014 at 2:22 pm

We have a few remarks.
– The material world is not unlimited
According to the Skanda Purana (2.2.27), there are 35 million universes in the material world.
Also in SB10.3.25 it says:
“After millions of years, at the time of cosmic annihilation, when everything, manifested and unmanifested, is annihilated by the force of time, the five gross elements enter into the subtle conception, and the manifested categories enter into the unmanifested substance. At that time, You alone remain, and You are known as Ananta Sesha-naga. ” Purport “After many millions of years, when Lord Brahma comes to the end of his life, the annihilation of the cosmic manifestation takes place. At that time the five elements—namely earth, water, fire, air and ether—enter into the mahat-tattva. The mahat-tattva again enters, by the force of time, into the nonmanifested total material energy, the total material energy enters into the energetic pradhana, and the pradhana enters into You. Therefore after the annihilation of the whole cosmic manifestation, You alone remain with Your transcendental name, form, quality and paraphernalia.”
If the material world is literally unlimited how Maha-Visnu can expand and take it in again every
6.22 trillion years.
This unlimited is figurative.

– The 1/4 and 3/4 energies of CC madhya 21.55
cic-chakti-vibhuti-dhama—tripad-aisvarya-nama
mayika vibhuti—eka-pada abhidhana
WORD-FOR-WORD MEANINGS
cit-sakti—of the spiritual energy; vibhuti-dhama—opulent abode; tri-pad—three fourths; aisvarya—opulence; nama—named; mayika vibhuti—material opulence; eka-pada—one fourth; abhidhana—known.
TRANSLATION
“The spiritual world is considered to be three fourths of the energy and opulence of the Supreme Personality of Godhead, whereas this material world is only one fourth of that energy. That is our understanding.
means vihutis-parts. This qualitative meaning is given in Laghu Bhagavatamrta 5.286; the Lord has 4 vibutis or excellences: 1. the spiritual energy of the spiritual world – the svarupa-sakti, 2. the Brahmajyoti, 3. the marginal energy and 4. the material world.
Or also we read 1. His original form, 2. the forms of His direct expansions, 3. the individual spirit souls, and 4. the world of matter.
Or 1. Krishna, 2. cit-sakti, 3. tatastha-sakti, 4. maya-sakti.

“tripad-vibhuter dhamatvat tripadbhutam tu tat padam
vibhutir mayiki sarva prokta padatmikayatah

TRANSLATION
Vaikuntha is called tripad-bhutam because it is the abode which possess three portions of power. All the powers of the material realm are called only one portion.

COMMENTARY (– Srila Baladeva vidyabhusana)
When Vaikuntha is described as tripad-bhutam it means that the material powers of the material realm consisting of one pad or segment, do not exist in Vaikuntha. (Rupa Gosvami– Laghu Bhagavatamrta 5.286)
1. Atmavidya Dasa says :
  
  Nov 21, 2014 at 10:23 am
  
  You wrote:
  
  “If the material world is literally unlimited how Maha-Visnu can expand and take it in again every
  6.22 trillion years. This unlimited is figurative. ”
  
  Material world doesn’t refer to just this universe but to the pradhana and maha-tattva which contain infinite number of material universes. Check the image at the top with quote from Brahma Samhita. Material world refers to the complete material manifestation not just our tiny universe, the smallest of all universes.
Gauragopala dasa says :

Nov 17, 2014 at 6:38 pm

One word, inconceivable! How can anyone work out 75% and 25% of infinity or eternity? The Spiritual World is endless and the material creation is a quarter of that. Yes it is inconceivable. And the number of jivas is also inconceivable in both Vaikuntha and the material World
1. Balakrsna das says :
  
  Nov 21, 2014 at 9:54 am
  
  The material world refers to the Pradhana and the Maha-tattva. It is indeed eternal and infinite and boundless but is not part of the spiritual world. It is the separated energy of the Lord. Most of this is discussed in the SB 3rd canto.
Patitapavana says :

Nov 18, 2014 at 3:09 pm

We just commented that the material world is NOT unlimited. The descriptions of the material world
being unlimited are figurative. In SB 1.3.1 Srila Prabhupada comments:
“The mahat-tattva is like the cloud in the clear sky. In the spiritual sky, the effulgence of Brahman is spread all around, and the whole system is dazzling in spiritual light. It is assembled in some corner of the vast, unlimited spiritual sky, and the part which is thus covered by the mahat-tattva is called the material sky. This part of the spiritual sky, called the mahat-tattva, is only an insignificant portion of the whole spiritual sky, and within this mahat-tattva there are innumerable universes.”
Clouds are not unlimited, otherwise they would be formless.
All such words in scripture eg sat, anadir, ananta, nitya can also be non-literal.
See the following examples:
– “When the sun-god and moon-god exposed the plot of wicked Rahu to steal the celestial nectar, a lasting (sasvata) enmity was sealed among them, which endures to the present day.” (Mbh. 1.17.8)
– “The five sons of King Vasu each became kings in their own right, all five establishing permanent (sasvata) dynasties bearing their names.” (Mbh. 1.57.30)
– “Defeated by his old friend Drona, King Drupada diplomatically solicits from him his ‘constant (sasvata) favor’ (Mbh. 1.128.13)
– “The brahmana host of the Pandavas at Ekacakra condemns the incompetent king of the region who cannot provide the people with sasvata safety from harm.” (Mbh. 1.148.9)
– Jaratkaru assures his forefathers that he will marry and beget a son who will preserve the family line and keep the forefathers in heaven:
“Surely for your deliverance offspring will arise in that [marriage]. May my forefathers enjoy, having reached the permanent status (sasvata-sthanam)!” (Mbh. 1.13.28)
– When King Indra of heaven convinces the earthly King Vasu to give up the attempt to take Indra’s position, Indra promises that by sticking to his earthly duties, Vasu will eventually attain to the sasvata worlds:
“Ever protect the dharma that will take you to higher worlds, engaged and with attention, for being so engaged in dharma you shall then attain the pious, everlasting worlds (sasvatan lokan).” (Mbh. 1.57.6)
– The sage Mandapala attempts to enter heaven on the strength of his pious credits, but he is turned back by the gatekeepers with these words:
“These very worlds are concealed from you because of [your lack of] progeny. Beget progeny and then you shall enjoy these everlasting (sasvatan lokan) worlds.” (Mbh. 1.220.13)
– After begetting good sons, the same Mandapala then offered this prayer to the fire-god, Agni, when the blazing inferno of Khandava threatened to consume his young sons:
“Offering obeisances unto you, the sages go with their wives and sons to the everlasting destination (sasvatim gatim), won by their own work.” (Mbh. 1.220.25)
– “After having ruled the citizens according to dharma for endless years (sasvatih samah), King Yayati, son of Nahusha, accepted a very ghastly old age that ruined his beauty.” (Mbh. 1.70.33)
– The Rakshasi Hidimba refused her hungry brother’s order to kill the Pandavas, reasoning that:
“If they are killed (and eaten), there will be but a moment’s satisfaction for my brother and me. But by not killing them (and thus marrying Bhishma), I will enjoy for endless years (sasvatih samah).” (Mbh. 1.139.16)
– When the Pandavas are defeated at dice, the wicked Duhsasana declares that Pritha’s sons have now been driven to hell for a long, virtually unlimited time, and that they are bereft of their happiness and kingdom, and ruined for endless years (sasvatih samah). (Mbh. 2.68.5)
– “Having achieved the worlds of the pious doers, and having dwelt there for endless years (sasvatih samah), a fallen yogi takes birth in the home of pure and opulent persons.” (Bg. 6.41)
– “One should eat very frugally and should always (sasvat) remain secluded so that he can achieve the highest perfection of life.” (Bhag. 3.28.3)
– “O Lord, with a corpselike body that is always (sasvat) fearful, we bear the burden of the dreamlike happiness of kings.” (Bhag. 10.70.28)
– “O almighty Lord, we shall no longer desire a mirage-like kingdom that is to be attentively served by a material body that is always (sasvat) declining, and is the source of sufferings.” (Bhag. 10.73.14)
– “The Pandavas have been driven into hell for an endlessly long time-dirgha-kalam anantakam. They have been deprived of their happiness and their kingdom. They are lost forevermore.” (Mbh. 2.68.5)
– “As a friend of Krishna, I alone with my chariot, crossed over the ocean of the Kuru army, an invincible ocean with no end [of the distance] to its far shore (ananta-param).” (Bhag. 1.15.14)
– (Bhag. 5.5.17), Lord Rishabhadeva warns His sons that a blind materialist does not see his own unlimited (or unending) misery (ananta-duhkham).
– Sukadeva Gosvami announces the benefits of the pumsavana vow, which is said to cause “unlimited satisfaction (ananta-triptih) for the forefathers and demigods” (Bhag. 6.19.27).
– “Formerly, O King, that very Supreme Lord expanded the reputation of Rudra, after that god’s fame had been struck down by Maya Danava, who possessed unlimited (ananta) mystic power.” (Bhag. 7.10.51)
– In Srimad-Bhagavatam 11.10.37, Uddhava says to Lord Krishna:
“The same, single entity is said to be eternally liberated and eternally conditioned. That is my confusion.”
– anadih—the firstborn, Lord Brahma
After being born, Daksha, by the superexcellence of his bodily luster, covered all others’ bodily opulence. Because he was very expert in performing fruitive activity, he was called by the name Daksha, meaning “the very expert.” Lord Brahma therefore engaged Daksha in the work of generating living entities and maintaining them. In due course of time, Daksha also engaged other Prajapatis [progenitors] in the process of generation and maintenance.
Lord Brahma anadi, “the beginningless one.” (SB 4.30.51)
– the demigods are described as amara immortal
– Srila prabhupada also sometimes uses these words non-literal.
“anadi karama-phale, which means that these actions and reactions of one’s activity cannot be traced, for they may even continue from the last millennium of Brahma’s birth to the next millennium.” (Bhag. 3.31.44, purport)
“Eternally conditioned means we do not know when we have been conditioned like this. ……. Many, many Brahma’s life. Not only one Brahma’s. There are so many Brahmas changed, and we are conditioned. So therefore we are called eternally conditioned.” (Cc. lecture, January 9, 1967, New York)
anadi karama-phale. Anadi. Anadi means… Adi means the creation. Creation… before creation, I [become] contaminated [with] this desire, iccha-dvesha samutthena.” (Bhag. lecture, January 1, 1975, Bombay)
Our comment: He simply explains here anadir as before the adi, beginning or creation.
Thus, the spiritual world IS unlimited, the material world is very, very big.
You can do the math for this article.
Mathematics as formulated by mortals can have infinities, since there is also mathematics in the spiritual world; mathematics is truth for all infinity.
1. Balakrsna das says :
  
  Nov 21, 2014 at 9:45 am
  
  Shyamasundara Prabhu gave numerous quotes substantiating that the material world infinitely large. The first quote is proof enough and he supplied others as well..
  
  “”The Maha-Vishnu, into whom all the innumerable universes enter and from whom they come forth again simply by His breathing process, is a plenary expansion of Krishna. Therefore I worship Govinda, Krishna, the cause of all causes.” Brahma-samhita 5.48″
  
  The unlimited Karanadakashayi Visnu is emanating infinite numbers of material universes from the infinites pores of his skin, not just 35 million. As the accompanying image suggests from each of the unlimited pores of His skin come a stream of infinite universes with one exhalation of the Lord. And they are all withdrawn again when he inhales.
Pusta Krishna das says :

Nov 19, 2014 at 6:18 am

The great wonder of this all is that Sri Krishna is our dearmost Friend and Well-wisher. Although He is the Creator, and He acknowledges that all of this springs from but a spark of His splendor, He crawls on the floor of the house of Nanda-maharaj, charming all by His beauty and attractive pastimes. Ultimately, we may, if fortunate, be blessed with jnana-sunya-bhakti, whereby Krishna exposes His supreme sweetness and love, hiding His unlimited greatness from the bhakta with whom He desires to exchange love. Hare Krishna.
Pusta Krishna das
1. Shyamasundara Dasa says :
  
  Nov 24, 2014 at 2:46 pm
  
  You are right it is amazing that the all powerful Krsna our dear most friend.
  
  In the Bg 10.12-13 Arjuna states that Krsna divine nature had been confirmed to the Pandavas by others before such as Devala, Asita, Narada and Vyasa.
  
  Makandeya Rsi was also one of those who had explained to the Pandavas that their cousin Krsna was God Himself. Markendeya Rsi had told his story about his experience with the Lord’s illusory potency to the Pandavas while there were in the forest. Krsna was also listening to the story. Here is last part of that chapter where he points out the real identity of Krsna.
  
  ‘Markandeya continued, ‘Having said so unto me that wonderful Deity vanished, O son, from my sight! I then beheld this varied and wondrous creation start into life. O king, O thou foremost of the Bharata race, I witnessed all this, so wonderful, O thou foremost of all virtuous men, at the end of the Yuga! And the Deity, of eyes large as lotus leaves, seen by me, in days of yore is this tiger among men, this Janardana who hath become thy relative! It is in consequence of the boon granted to me by this One that memory doth not fail me, that the period of my life, O son of Kunti, is so long and death itself is under my control. This is that ancient and supreme Lord Hari of inconceivable soul who hath taken his birth as Krishna of the Vrishni race, and who endued with mighty arms, seemeth to sport in this world! This one is Dhatri and Vidhatri, the Destroyer of all the Eternal, the bearer of the Sreevatsa mark on his breast, the Lord of the lord of all creatures, the highest of the high, called also Govinda! Beholding this foremost of all gods, this ever-victorious Being, attired in yellow robes, this chief of the Vrishni race, my recollection cometh back to me! This Madhava is the father and mother of all creatures! Ye bulls of the Kuru race, seek ye the refuge of this Protector!’
  
  Vaisampayana continued, “Thus addressed, the sons of Pritha and those bulls among men–the twins, along with Draupadi, all bowed down unto Janardana. And that tiger among men deserving of every respect thus revered by the sons of Pandu, then consoled them all with words of great sweetness.”
Shyamasundara Dasa says :

Nov 24, 2014 at 2:02 pm

Hare Krsna.

Some doubts have been expressed by the purva-paksa. To present the siddhanta on this topic I request the reader to refresh their memory by reading Caitanya Caritamrta 2.21 http://www.vedabase.com/en/cc/madhya/21

Srila Bhaktivinoda Thakura gives the following summary of the twenty-first chapter. In this chapter Sri Caitanya Mahaprabhu fully describes Krsnaloka, the spiritual sky, the Causal Ocean and the material world, which consists of innumerable universes. Sri Caitanya Mahaprabhu then describes Lord Brahma’s interview with Krsna at Dvaraka and the Lord’s curbing the pride of Brahma. There is also a description of one of Krsna’s pastimes with Brahma. In this chapter the author of the Caitanya-caritamrta has presented some nice poems about the pastimes of Krsna and Krsna’s superexcellent beauty. Throughout the rest of the chapter, our intimate relationship (sambandha) with Krsna is described.

Here are few salient verses, the kind reader is requested to read the whole text including purports.

As you will find Lord Caitanya Mahaprabhu’s opinion is that the material world is composed of innumerable (infinite) universes (not a mere 35 million which is a countable number). And that no one can measure the one fourth of His energy what to speak of the three fourths. It is not an exaggeration to say the material manifestation is infinite.

“Krsna said, ‘Your particular universe has a diameter of four billion miles; therefore it is the smallest of all the universes. Consequently you have only four heads.

“ ‘Some of the universes are one billion yojanas in diameter, some one trillion, some ten trillion and some one hundred trillion yojanas. Thus they are almost unlimited in area.

“ ‘According to the size of the universe, there are so many heads on the body of Brahma. In this way I maintain innumerable universes [brahmandas].

“ ‘No one can measure the length and breadth of the one fourth of My energy manifested in the material world. Who then can measure the three fourths that is manifested in the spiritual world?’

“ ‘Beyond the river Viraja is the spiritual nature, which is indestructible, eternal, inexhaustible and unlimited. It is the supreme abode, consisting of three fourths of the Lord’s opulences. It is known as paravyoma, the spiritual sky.”’

CC 2.21.84-88
1. Patitapavana says :
  
  Dec 11, 2014 at 9:44 pm
  
  We studied Caitanya Caritamrta madhya 21
  Verse 85 is “Some of the universes are one billion yojanas in diameter, some one trillion, some ten trillion and some one hundred trillion yojanas. Thus they are almost unlimited in area.”
  ‘Almost unlimited’ means the word ‘unlimited’ is used figuratively. ‘Almost unlimited’ means somewhat bigger than one billion, one trillion, ten trillion, one hundred trillion, would be innumerable, uncountable or unlimited.
  
  If the material world would be unlimited, then there would be unlimited souls in the material world. Also because His Divine Grace Srila Prabhupada told to purvapaksa His Grace Syamasundara prabhu in conversations 17-10-71 that all the material atoms are souls.
  But there are no unlimited souls in the material world, only a few. Why would the spiritual world need an unlimitedly big prison= Durga, the citadel of DurgA. There are only a few rascals to be kicked out of the spiritual world, to the material world. If the amount of rebellious souls is unlimited, God made a mistake in expanding them; He has caused unlimited suffering.
  And, His Divine Grace Srila Prabhupada, savior of the whole eka-pada world, said there are only a few souls here:
  
  “The plan of material world is that some rascals, living entities, they wanted to enjoy. So God has given this plan, “All right, you enjoy.” This is the plan. And not only enjoy. “You enjoy; again come back.” This is the plan. Pravrtti-nivrtti. First of all he is given that “All right, you take all facilities of enjoyment.” Therefore Veda is that “You enjoy like this, and after you have fulfilled your enjoyment, come back again.” This is God mercy…The result is that he becomes more attached to this temporary world and remains the rascal. Because without being rascal, nobody comes in this material world to enjoy. As soon as anyone has come to this material world, he’s a rascal. Krsna-bahirmukha hana bhoga vancha kare, nikata-stha maya tare japatiya dhare (Prema-vivarta).” (Morning Walk, December 16, 1973, Los Angeles)
  
  “He’s already an ass because he’s part and parcel of Krsna, and he has come to this material world to enjoy. That is ass mentality. There is no enjoyment. So he’s already an ass. And this scientific improvement means he’s becoming more attached to this material world to remain better ass. Avidya… anitya samsare, anitya. He cannot stay here. Suppose, working very hard like an ass, he gets a skyscraper building, throughout his whole life, laboring. But he cannot stay there. He’ll be kicked out. Is it not ass? Is he not an ass? He cannot stay there. Anitya samsare. Anitya. Because it is not the permanent settlement. You are trying: dum dum. (sound imitation) Very strong foundation. That’s all right. But your foundation is nothing. You’ll be kicked out.” (Morning walk Los Angeles, April 28, 1973)
  
  “And there are innumerable spiritual living entities also. And some of them, those who are not fit to live in that spiritual world, they are sent to this material world. The same idea is expressed in Milton’s Paradise Lost. So we, all conditioned souls, we are practically living in a place after Paradise Lost.” (Lecture, April 23, 1969, Buffalo, New York)
  1. Balakrsna das says :
    
    Dec 13, 2014 at 2:28 am
    
    Dear Prabhu,
    
    Hare Krsna.
    
    It appears that you have misapprehended what the definition of “material world” or “material sky” means. It is not one particular universe no matter how big or small it may be. You seem to think the material world refers to one particular universe. And that when it refers to infinite that that universe is infinitely large. No, that is not the case. What is meant by infinite is that there infinite universes that are emanating from Mahavisnu – not just one universe.
    
    The material sky is the aggregate of all material energies and it contains infinite and unlimited universes, not just one. Just as in the spiritual sky there are unlimited spiritual planets. They are not limited.
    
    And while it is true that the material world is infinite and unlimited it shrinks to the diameter of the footprint of a calf when we become truly Krsna Conscious.
    
    Anyway I hope this gives to a clearer understanding. There are infinite number of material universe, not that a particular material universe is infinitely large. There is a big difference.
  2. Somayaji says :
    
    Dec 13, 2014 at 10:41 pm
    
    Patita Pavana Prabhu wrote:
    
    ‘“Verse 85 is “Some of the universes are one billion yojanas in diameter, some one trillion, some ten trillion and some one hundred trillion yojanas. Thus they are almost unlimited in area.”
    
    ‘Almost unlimited’ means the word ‘unlimited’ is used figuratively. ‘Almost unlimited’ means somewhat bigger than one billion, one trillion, ten trillion, one hundred trillion, would be innumerable, uncountable or unlimited.’
    
    The first paragraph is quoted from CC 2.21.85, the second is his comment. In his comment Prabhu stresses on the largest universe and surmises somehow that this is the “material world.” And in this case points out that the biggest of the universes is “almost unlimited in area” and therefor finite. And, it is true that even the biggest material universe is finite, there is no argument here. But one material universe is not the whole of the material creation. This is the point. What about all the other unlimited material universes? The whole of material creation is the mahattatva and pradhana and all of the material universes that emanate from Karanadakasayi Mahavisnu – see image at the beginning of the article.
    
    The Brahma Samhita and other sastras tell us that from this Mahavisnu infinite universes emanate not just one or 35 million, but infinite numbers of universes.
    
    “The Maha-Vishnu, into whom all the innumerable universes enter and from whom they come forth again simply by His breathing process, is a plenary expansion of Krishna. Therefore I worship Govinda, Krishna, the cause of all causes.”
    Brahma-samhita 5.48
    
    And Bhaktivinode Thakura in his comments on CC 2.21 states “the material world, which consists of innumerable universes.” Notice he says “innumerable universes” not just one universe.
    
    Hence it is not a matter of how big or small a particular finite material universe is but the fact that there are infinite number of universes and that all of these material universes make up the material world not just one universe.
Shyamasundara Dasa says :

Nov 24, 2014 at 2:10 pm

For those of you who wanted a more complete proof that the Real Numbers R ={0<x<1} is a bigger size of infinity than the set of (integers) Natural Numbers N= {1, 2, 3, 4, …} here is an easy to understand article on the topic:

Here’s The Simple Proof That There Must Be Multiple Levels Of Infinity

http://www.businessinsider.in/Heres-The-Simple-Proof-That-There-Must-Be-Multiple-Levels-Of-Infinity/articleshow/25810736.cms
Patitapavana says :

Dec 7, 2014 at 9:13 pm

We are not purvapaksa.
The writer of this “many infinities..” is the purvapaksa or opponent; he started to change the siddhanta which was always clear.
Here are some quotes mainly from the Vedabase:

Bhaktivinoda Vani Vaibhava, 24.7 7. Can the living entity understand that the spiritual world exists within the material world but remains untouched by matter?
Poor human understanding cannot possibly make out how the extensive triquadrantal, which is beyond human comprehension, can be accommodated in the limited material universe of a uniquadrantal disclosure. Gokula is a spiritual plane, hence its condescended position in the region of material space, time, etc., is in no way restricted but unlimitedly manifested with its full boundless propriety.

Thus the “uniquadrantal” or eka-pada is a limited area.
Because this refers to the 1/4 or one of the 4 vaibhavas, bhutas or vibhuti segments (pada)
See:
Amnaya Sutra Sutra 8 – Srila Bhaktivinoda Thakura

“svarupa-tad-rupa-vaibhava-jiva-pradhana-rupena tac caturdha

svarupa-own form; tad-rupa-vaibhava-expansions; jiva-individual spirit souls; pradhana-matter; rupena-in the form; tat-that; caturdha-in four ways.

He has four manifestations: 1. His original form, 2. the forms of His direct expansions, 3. the individual spirit souls and 4. the world of matter.

In Bhagavata-sandarbha anuccheda16
Srila Jiva Gosvami explains:

ekam evam paramam tattvam svabhavikacintya-saktya sarvadaiva svarupa-tad-rupavaibhava-jiva-pradhana-rupena caturdhavatishthate.

“Although the Supreme Persoanlity of Godhead is one, by His inconceivable potencies He always has four manifestations: 1. His original form, 2. the forms of His direct expansions, 3. the individual spirit souls and 4. the world of matter.”

Studying the Caitanya Caritamrta verses about this
“Madhya-lila, Chapter 21: The Opulence and Sweetness of Lord Sri Krishna
TEXT 52
tara tale ‘bahyavasa’ virajara para
ananta brahmanda yahan kothari apara
WORD-FOR-WORD MEANINGS
tara tale—below the spiritual world; bahya-avasa—external abode; virajara para—on the other side of the river Viraja; ananta brahmanda—unlimited number of universes; yahan—where; kothari—apartments; apara—unlimited.
TRANSLATION
“On the other side of the river Viraja is the external abode, which is full of unlimited universes, each containing unlimited atmospheres.”

But our Brahmanda is not unlimited; again unlimited is figurative.

“Some of the universes are one billion yojanas in diameter, some one trillion, some ten trillion and some one hundred trillion yojanas. Thus they are almost unlimited in area.” (CC Madhya 21.85)
‘Almost unlimited’ again means figurative.

“The gist of this verse is: “O Lord, this material world manifested from the maya potency is limited and it is in constant flux. On the other hand, Your personal form is perfectly pure and spiritual.” (SB 10.14.22, Sarartha Darsini by Visvanatha Cakravarti Thakura)

The materialist becomes frustrated in his attempts to enjoy himself in the limited material world, he may seek impersonal liberation by merging either with the Causal Ocean or with the impersonal brahma-jyoti effulgence. However, as neither the Causal Ocean nor the impersonal brahma-jyoti effulgence affords any superior substitute for association and engagement of the senses, the impersonalist will fall again into the limited material world to become entangled once more in the wheel of births and deaths, (SB 2.2.31 purport by Srila Prabhupada)

In describing the Kasira Mayavadis, Srila Bhaktisiddhanta Sarasvati Thakura has explained that persons who are bewildered by empiric knowledge or direct sensual perception, and who thus consider that even this limited material world can be gauged by their material estimations, conclude that anything that one can discern by direct sense perception is but maya, or illusion. (CC Adi 7.39 purport by Srila Prabhupada)

Prabhupada: (indistinct) limited science, when you are in the limited material world, good means which satisfies my senses good. (SP Philosophical discussions with Syamasundar on Ludwig Wittgenstein)

SB 2.5.18 p: “As the sun is ever increasingly unaffected by a spot of cloud, so also the unlimited Lord is unaffected by the spot of material energy manifested at times in the unlimited span of the Lord’s rays of brahma-jyoti.”
The spot is a limited area
“The material creation is something like a cloud in the unlimited sky. The real sky is the spiritual sky, eternally filled with the rays of the brahma-jyoti, and a portion of this unlimited sky is covered by the mahat-tattva cloud.” (SB 2.5.21 p)
“This material world is an insignificant portion of the spiritual world that is covered by the material energy.” (The Laws of Nature: An Infallibele Justice, God and The Law of Karma)
“Therefore there are millions and billions of liberated souls above this material world, just like there is millions and billions of miles’ sunshine above the cloud. You go by airplane above the cloud. Oh, the cloud is, appear to be very insignificant. But sunshine? Oh, so nice, sunshine. Similarly, when you are above this material world, jyotir gamah… Jyotir gamah. Tamasi ma. The Vedanta, the Vedas inform you that “Don’t remain in this darkness. Just try to get out of it.” Jyotir gamah. Similarly… Just like the same way, airplane. As soon as you penetrate the cloud and go to the sky, you’ll see: “Oh, there is immense sunshine.” But while you are in, within the covering of the cloud, you say, “Oh, there is no sunshine today.” (Lecture, CC Adi7.118-121)
“Very insignificant” is not unlimited

“suppose the sky on San Francisco is overcast with cloud. We say that then we are covered in cloud. Practically this San Francisco sky is only a fragmental portion of the whole sky. Similarly, the real sky is that spiritual sky, paravyoma. When that paravyoma partially is clouded with mahat-tattva, that is called material world. This is the position of material world. Material world is also existing in the spiritual world, but it is covered and in a fragmental segment”. (Lecture, SB 1.3.1-3 SF 1968)
An insignificant portion of the sunshine may be covered, or is covered sometimes by the cloud. Similarly, this material world is an insignificant portion of the spiritual world, covered by this material energy. (Lecture on ISO mantra 1, 1970)
The mahat-tattva is assembled in some corner of the vast, unlimited spiritual sky, and the part which is thus covered by the mahat-tattva is called the material sky. This part of the spiritual sky, called the mahat-tattva, is only an insignificant portion of the whole spiritual sky, (SB 1.3.1 p)

Sri Brahma-samhita 5.10 The person embodying the material causal principle, viz., the great lord of this mundane world [Mahesvara] Sambhu, in the form of the male generating organ, is joined to his female consort the limited energy [Maya] as the efficient causal principle. The Lord of the world Maha-Vishnu is manifest in him by His subjective portion in the form of His glance.
purport
…By the power of His spiritual energy a plenary subjective portion of Him, eternally reposing in the neutral stream of Viraja forming the boundary between the spiritual and mundane realms, casts His glance, at creation, unto the limited shadow potency. Maya, who is located far away from Himself.
But then in Sri Brahma-samhita t 13 purport he states: “When those golden sperms, coming out with the exhalation of Maha-Vishnu, enter into the unlimited accommodating chamber of the limited potency (Maya) they become enlarged by the nonconglomerate great elements.”

Because the material world is very very large, but not literally unlimited

“We are put into this prison house, all these rebelled souls…. Caitanya Mahaprabhu said that this universe is just like a mustard seed in the bag of mustard seeds. You just imagine in a bag how many mustard seeds you can pack. Unlimited. You cannot count. Mustard seed within a bag, two and a half mounds weight. Can you count? No, it is not possible. Similarly all these universes, material universes, each of them is compared with a mustard seed, and this universe which we experience is one of the mustard seeds within the bag of mustard seeds….. Just like in the jail, the population in the jail is very small in comparison to the population of the city.
Similarly, within this material world, all the living entities, they are all conditioned, very limited number. The unlimited number are there in the spiritual world. (SB lecture, Mayapur, June 20, 1973)

If we want, artificially, more power to imitate Krsna, then we are gone. …just imagine how many liberated living entities are there. …. Just like in the jail, the population in the jail is very small in comparison to the population of the city. (Srimad-Bhagavatam 1.10.5, June 20, 1973, Mayapur)

And we small quantity, we misused our independence. We wanted to enjoy separately. Therefore we are conditioned.
… We are only simple few, this material world. Just like I have several times told you that the prison house. The population of prison house is nothing in comparison to the whole population. What is there? Suppose in New York there is a prison house. Oh, what may be the number? A few thousand maybe. But here, millions. Similarly, the liberated souls are millions; we are only few thousands, or hundreds. .. We are thinking this universe is very great. It is nothing in comparison to the whole creation of the Lord. You are seeing only universe, but there are millions of universes like this. …This is only a part of Krishna’s creation. One devotee of Lord Caitanya, requested, “My dear Lord, You have come to deliver all the fallen souls. You please take all the conditioned souls of this universe, and if You think they are not competent, they are sinful, You can give me all the sin to me. I shall suffer for them, but You kindly take.” So this is the desire of a pure devotee, that “All may go with Krishna. Let them become liberated. I shall suffer all their…” Now, Caitanya Mahaprabhu replied that “Suppose I keep your request. I take these, all the living entities of this universe. Do you think, is there any loss of this material world? It is just like a one mustard seed in the bag of mustard seeds.” So this universe is just like one mustard seed in one big bag of mustard seeds. Can you count how many mustard seeds are there in a big bag? So the idea was that Caitanya Mahaprabhu replied that “Even this universe is delivered fully, oh, there is a big bag of mustard seeds. It is only one grain.” There are so many conditioned souls, and these conditioned souls are only insignificant in comparison to the liberated souls. Just imagine what is the quantity of liberated souls. (Lecture, Sri Caitanya-caritamrita, Adi-lila 7.108, February 18, 1967, San Francisco)

One mustard seed is calculated to be a universe itself. In one of the universes, in which we are now living, the number of planets cannot be counted by human energy, and so how can we think of the sum total in all the universes, which are compared to a bucketful of mustard seeds? (SB 2.6.18 p)

“Maya and her unlimited material universes are situated in that Causal Ocean. Indeed, maya appears to be floating like a pot filled with mustard seeds.” (CC Madhya 15.176)

This analogy of the mustard seeds in a bag appears 19 x in the Vedabase.
Bags are never unlimited areas.

“Sri Satacandranana said: O demigod Brahma, millions of universes bob up and down (in the Karana ocean). As you are demigods in one universe, so in each each universe there are many demigods. You do not even know their names. When did you even meet them? Never leaving your own homes, you remain happy with stunted minds. You know one universe. Living entities are born in many universes, like mosquitoes in many udumbara fruits.”
Sri Narada said: Mocked in this way, the demigods were silent. (Garga– samhita 1.2 26-29 )

“They are in the spiritual world. Just like the number of population outside the prison house is very great, and the number of population within prison house is very small, this material world is supposed to be the prison house. Those who are condemned, those who want to try to lord it over, they are imprisoned within the walls of material universe. So their number is very small.” (Srimad-Bhagavatam 1.2.6, August 3, 1968, Montreal)

Prison are always a very small part of the whole state
“Still, although we are put into this prison house, all these rebelled souls, this prison house, this material world, is only one fourth of Krishna’s creation. Ekamsena sthito jagat [Bg. 10.42]. Ekamsena. The three-fourths part of His creation is the spiritual world. Just imagine, this ekamsa. Ekamsa means not only this one universe….in the jail, the population in the jail is very small in comparison to the population of the city. (Srimad-Bhagavatam 1.10.5, June 20, 1973, Mayapur)

Eka amsa is a part. 1/4 here means the maya-vibhuti

“In the spiritual world the number of liberated person—many, many times greater than these conditioned soul. Just like the prison house and outside the prison house. The population outside the prison house, their number is very great, but within the prison house there are small number, criminals.” (Bhagavad-gita 2.15, February 15, 1975, Mexico City)

“If you go to the prison house you will find so many people. But what are the proportions? These criminals who are put in together are a very small proportion.”
(Srimad-Bhagavatam 6.3.11–12, Allahabad, February 2, 1971 )

In the Spiritual World the number of individual souls are far far greater than what they are here. The conditioned souls are just like prisoners, as we have got less population in the prison house, similarly, in the material world the number of individual souls are very small. (Letter to: Mukunda, New York, 5 May, 1967, 67-05-05)

“Just as a madman becomes crazy and is put into a lunatic asylum, so we, losing sight of our spiritual identity, become crazy and are put into this material world. Thus the material world is a sort of lunatic asylum..” (Perfection of Yoga 3)

Lunatic asylums are always a small part of the whole state.

“Just like sometimes some of us becomes crazy and he is, goes to the lunatic asylum, similarly, those who become crazy, such spiritual identities, they are put into this lunatic asylum. It is called material world. This is a sort of lunatic asylum. Everything is being done not very sanely. [laughter] You see? [chuckling] So we have to get out of this lunatic asylum and enter into the kingdom of God, Sri Krishna.” (Bhagavad-gita 6.11-21, September 7, 1966, New York)

These rascals do not know that they are themselves bound up, and yet they are giving theory. The whole world is surrounded by all these rascals. We have to devise the means, “Please come here and take a little mercy. Sit down. Read a book.” We have to work for that. Don’t become angry by this lunatic asylum; otherwise the preaching will be finished. (31. Prabhupada Said: on Sannyasa, Preaching to Fools, Scientists and Dreams)

Out of that unlimited expansion of minute portions-jivas- of the Supreme Lord, some are covered by the influence of material nature, whereas others are free. (Krishna book chapter twenty, Description of Autumn)

Generally, people are bewildered by the activities of scientists and technologists. Due to maya they think that there is no need of God and that they can do everything and anything, but actually they cannot. Since this cosmic manifestation is limited, their existence is also limited. Everything in this material world is limited, and for this reason there is creation, sustenance and dissolution. However, in the world of unlimited energy, the spiritual world, there is neither creation nor destruction. (CC Adi-lila TEXT 116 PURPORT)
1. Balakrsna das says :
  
  Dec 11, 2014 at 11:32 pm
  
  Shyamasundara Prabhu provided explicit quotes and gave very clear and direct explanations that are easy to understand. You have not. We are reminded of Lord Caitanya’s pastime with Sarvabhauma Bhattacarya:
  
  “My dear sir,” the Lord replied, “as far as the Vedānta-sūtra itself is concerned, I can understand the meaning quite well. But I cannot understand your explanations. There is nothing difficult about understanding the meaning of the original aphorisms of the Vedānta-sūtra, but the way you explain them obscures the real meaning. You do not elucidate the direct meaning but imagine something and thus obscure the true meaning. I think that you have a particular doctrine you are trying to expound through the aphorisms of the Vedānta-sūtra.” http://www.vedabase.com/en/tlc/24
2. Somayaji says :
  
  Dec 12, 2014 at 12:21 am
  
  Dear Prabhu,
  
  Hare Krsna.
  
  Don’t mind me saying this. But the whole point of this article was in relation to the Lords infinite creation. It is understood that the Lord’s creation is infinite, and unlimited; and explained in purusha sukta and other sastras that this unlimited creation is divided into 3 parts spiritual and 1 part material. And even though all the quotes provided by Shyamasundara Prabhu clearly indicate that both the material creation and spiritual creation are unlimited and eternal it is still possible that one is 3 times larger than the other, that is how infinity works as it says in the Isa Upanishad
  
  The Personality of Godhead is perfect and complete, and because He is completely perfect, all emanations from Him, such as this phenomenal world, are perfectly equipped as complete wholes. Whatever is produced of the Complete Whole is also complete in itself. Because He is the Complete Whole, even though so many complete units emanate from Him, He remains the complete balance. http://www.vedabase.com/en/iso
  
  However, by your insisting that the material creation is limited and finite therefore implies that since 1 part is finite the other 3 parts are also finite. This is an absurd conclusion.
  
  One way of looking at is is to say that since compared to the spiritual creation the material creation is smaller so in that way we can say it is limited. But a direct reading of the slokas do suggest that the material world is infinitely large and uncountable. Yet it is smaller than the spiritual creation.
  
  These matters are beyond the capacity of infinitesimally small spirit souls to understand. We must, as Vedanta Sutra 1.1.3 points out, simply accept the statement of sastra on these points.
Sita Rama 108 says :

Dec 13, 2014 at 4:20 am

I can’t follow the mathematical formulas but it is simple logic that the set of even whole numbers is infinite, the set of all whole numbers is a greater infinity, and neither is the complete set of numbers. This is child’s play. There is a TV commercial where an adult asks nine year old kids what is greater than infinity. The first says infinity plus one- the next says, infinity plus infinity- next, infinity times infinity- next, infinity to the infinite power. But from the Veda’s we know, beyond synthetic logic, that the complete infinity is Krishna who has an infinite variety of infinity potencies, of which three are chief.
I would like to see research on whether the 1/4 example is literal or just meant to give us an idea. There are examples of such things. The soul is said to be one ten thousandth the tip of a hair but we know that even the material mind, intelligence and false ego are more subtle than material space and thus have no dimension. Therefore it follows the soul has no material dimension either. Also, sometimes the Supersoul is said to be the size of ones thumb.
1. Shyamasundara Dasa says :
  
  Dec 15, 2014 at 11:05 am
  
  Sita Rama 108 said:
  
  “I can’t follow the mathematical formulas but it is simple logic that the set of even whole numbers is infinite, the set of all whole numbers is a greater infinity, …”
  
  If you did follow the mathematical logic then you would understand that actually they are the same size. Not that one is greater than the other. Why? Because they are “countably infinite” thus you can make a one to one correspondence between them. 1 –> 2, 2–>4, 3–>6, 4–>8, 5–>10,… to infinity.
  
  I would like to see research on whether the 1/4 example is literal or just meant to give us an idea.
  
  This 1/4 example is cited everywhere in sastra, from the Vedas, to the puranas and to texts as recent as Caitanya Caritamrta. Srila Prabhupada said some something to the effect that in the sastras it says that there are exactly (quotes number) so many aquatics we accept that, not something more or less. So Srila Prabhupada put his trust in the sastras, that they were not trying to give us an idea. Because the sastras are coming directly from Krsna and Krsna knows the actual situation.
Patitapavana says :

Dec 17, 2014 at 11:16 am

One Bhakta purvapaksa quoted Isopanisad
om purnam adah purnam idam
purnat purnam udacyate
to explain that the material world is complete meaning infinite. Here is what Srila Prabhupada says in the introduction to this Isopanisad:
“The Vedas are sabda, or spiritual sound vibration, and are the best form of evidence. They can even reveal the spiritual realm, far beyond this limited material world, and this is accepted by such great authorities as Ramanujacarya, Madhvacarya and Vishnusvami, and even by the famous Mayavadi leader, Sankaracarya.”

Here is one quote from Acarya Madhva, he says:
“……if different activities are naturally attributed to different personalities according to their natures, then where really is the question of free will to act? Given a specified field of activities with a set of previously defined options, or perimeters there is only so much that one will naturally chose to do according to one’s nature. This material world is after all limited, even though due to our limited vision it seems like a vast realm of variety, but there is only so much here in a temporal dream.”(quote Dattaswatantrya, Ontology.).

Some more Quotes from the Acarya’s

Bhagavat sandarbha -Sri Jiva Gosvami Anuccheda 73.8 “Beyond this darkness, beyond the ether element, and beyond the boundary of the material universes is the Lord Siva’s great transcendental abode, which even the great demigods cannot approach. This is clearly described in the Sruti-sastra.”

Limited areas have boundaries. The material world is a specific demarcated tamah-dhama.

Krishna sandarbha Anuccheda 106, Text 31 “Pancasititama-patala in the Svayambhuva-agama, where Lord Siva says to Gauri:

tatas ca brahmano lokam brahma-cihnam smaret sudhih urdhve tu simni virajam nihsimam vara-varnini

tatah – from that; ca – also; brahmanah – of Lord Brahma; lokam – the planet; brahma-cihnam – the marks of spirituality; smaret – should remember; sudhih – an intelligent person; urdhve – above; tu – also; simni – on the border of the spiritual and material worlds; virajam – the Viraja river; nihsimam – unlimited; vara-varnini – O fair-complexioned Parvati.

Below this original feature of the three modes of nature is the planet of Lord Brahma, which is full of all symptoms of spiritual awareness. O fair-complexioned Parvati, an intelligent person should meditate on this planet, and also on the unlimited Viraja river, which forms the boundary of the spiritual and material worlds.”

Bhagavad sandarbha Anuccheda 10 Lord Siva explains (Padma Purana, Uttara-khanda 255.56.59):
19 “My dear Parvati, you have just heard about the opulences of the material energy, now hear about the supreme opulences of the spiritual world, which comprises three quarters of all existence.
20 “Produced from the perspiration of the Personality of Godhead, whose limbs are all the Vedic literatures, the auspicious Viraja River flows on the boundary that separates the material energy from the spiritual sky.
21 “On the farther shore of the Viraja River is the spiritual sky. In that spiritual sky I the abode of the Supreme Personality of Godhead. That abode is eternal, imperishable, unlimited, effulgent, transcendental, and full of nectar. That abode is made of the transcendental energy known as the mode of pure goodness (suddha-sattva).”

“That original Personality of Godhead, named Sankarshana, first lies down in the river Viraja, which serves as a border between the material and the spiritual world. As Karanodakasayi Vishnu, He is the original cause of the material creation.” ( CC Mad. 20.268)

“The Viraja, or Causal Ocean, is the border between the spiritual world and material worlds. The material energy is situated on one shore of that ocean, and cannot enter onto the other shore, which is the spiritual sky.” (Cc. Mad. 20.269)

“The sole potency of Krsna which is spiritual, functioning as Krsna’s own proper power, has manifested His pastimes of Goloka or Gokula. By her grace individual souls who are constituents of the marginal potency can have admission into even those pastimes. The deluding energy, who is of the nature of the perverted reflection of the spiritual (cit) potency, has got her location on the other side of the river Viraja, which surrounds the Brahma-dhama forming the boundary of Maha-Vaikuntha as the outer envelope of Goloka. The position of Goloka being absolutely unalloyed with the mundane, deluding energy, far from having any association with Krsna, feels ashamed to appear before His view.” (Brahma samhita purport to 5.6)

“Lying in the causal water as the primal purusa-avatara He casts His glance towards Maya (the limited potency).“ (Brahma samhita purport to 5.8)

The limited realm.

“The full quadrantal extension of the Supreme Lord, is His majesty. Of this the triquadrantal extensions of unlamenting, nonperishing and nonapprehending situations constitute the majesties of the realms of Vaikuntha and Goloka, etc. In this temporal realm of Maya devas and men, etc.-all these together with all mundane worlds-are the great majesties of the limited potency.” (Bs 5.9 purport)

The person embodying the material causal principle, viz., the great lord of this mundane world [Mahesvara] Samhhu, in the form of the male generating organ, is joined to his female consort the limited energy [Maya] as the efficient causal principle. The Lord of the world Maha-Visnu is manifest in him by His subjective portion in the form of His glance. (Bs 5.10)

“Maha-Sankarshana, subjective plenary facsimile of the extended personality of Sri Narayana, is also the divine plenary portion of the propagatory embodiment of Sri Krishna. By the power of His spiritual energy a plenary subjective portion of Him, eternally reposing in the neutral stream of Viraja forming the boundary between the spiritual and mundane realms, casts His glance, at creation, unto the limited shadow potency. Maya, who is located far away from Himself.” (Bs 5.10. purport)

“The Karana Ocean, which is also known as the Viraja River, lies on the boundary that separates the spiritual and material worlds.” ( Jaiva dharma. Chapter Thirteen, Nitya-dharma O Sambandhabhidheya-prayojana (Pramana-vicara O Prameya Arambha)

“Within that one quarter of the Lord’s opulences exist the material universes that have fourteen planetary systems. On the boundary that divides the material and spiritual world flows the Viraja river. On the father shore of the Viraja is the spiritual world.” (Chapter Thirty-one, Madhura-rasa-vicara, Madhura-rasa – Jaiva dharma)

“…the Absolute Truth is not matter and the Absolute Truth is not materially restricted by limited potency.” (KB Ch 13, The Stealing of the Boys and Calves by Brahma)

“Now this universe, this material world is called Devi-dhama. Devi-dhama. It is under the control of the material energy. Srsti-sthiti-pralaya-sadhana-saktir-eka chayeva yasya bhuvanani vibharti durga [Bs. 5.44]. This energy is also personified called Durgadevi. So above this planetary system there is Mahesa-dhama. Mahesa-dhama. In the border between spiritual sky and material sky. Above that, there are Hari-dhama, the Vaikuntha planets where Narayana, in various forms is predominating.” (Lecture by SP, “Purpose Of Installing Deity,” 21 Aug 73 , London)

IF the Material World would be UNLIMITED, IT WOULD PERVADE THE Spiritual World WITH ITS UNWHOLESOMENESS , BUT BHAGAVATAM SAYS THERE IS NO MODES OF NATURE IN THE Spiritual World.

“In the Vaikuntha planets is the Supreme Personality of Godhead, who is the original person and who can be understood through the Vedic literature. He is full of the uncontaminated mode of goodness, with no place for passion or ignorance.” (SB 3.15.15.)

In that personal abode of the Lord, the material modes of ignorance and passion do not prevail, nor is there any of their influence in goodness. There is no predominance of the influence of time, so what to speak of the illusory, external energy; it cannot enter that region…” (SB 2.9.10.)

Chant Hare Krishna, Hare Krishna, Krishna Krishna, Hare Hare/ Hare Rama, Hare Rama, Rama Rama, Hare Hare and transcend the limited, finite to ascend to the unlimited, infinite.
Patitapavana says :

Apr 21, 2015 at 7:34 am

The purvapaksa opened his article with a sloka from
Rig veda

etavanasya mahima-ato jyayash-ca purushah
pado-asya vishva bhutani tri-pad-asya-amrtam divi
tri-pad-urdhva udait-purussah pado-asye’ha-abhavat-punah
tato vishvang vya’kramat-sashana-anashane abhi
“All beings make up only one-quarter of Him. Three-quarters of Him which are immortal are in Heaven. Three-quarters of the Purusha ascended high; one-quarter was here, again and again. And, diversified in form, it moved to the animate and inanimate world.” (Purusha Sukta1.3-4 from Rig Veda 10.90)

Srila Visvanatha Cakravarti Thakura gives the purport to this sloka in his Sarartha Darsini tika on Srimad Bhagavatam 2.6.19-23
SB 2.6.19-20 says: The 3 vibhuti’s are amritam—deathlessness or nectar; kshemam— welfare, all happiness, free from the anxiety of old age, diseases, etc.; abhayam—fearlessness. The one vibhuti, quality of the material world is death. (dictionary meaning and Bhaktivedanta vedabase gives for vibhuti: glory, prosperity, opulence, specific powers, riches, expansion, effulgence etc.) Nothing with quantity. Tika: “Two verses distinguish the material and spiritual vibhutis. The wise know that all living beings, whether conditioned or liberated, reside within either the material or spiritual portions (padeshu) of the Lord…In the places in the spiritual sky…there is no death (amrtam), no sickness (kshemam), and no fear (abhaya) arising from offenses to the Lord among the persons there. Absence of fear from time is already covered in the word amritam. This is established (adhayi) there. In the place of the three gunas, death, sickness and fear of offense are well established…This verse (SB 2.6.19) explains the Purusha-sukta phrases pado ’sya visva-bhutani tripadasyamritam divi: the living entities of the universe are one quarter and in the spiritual world of three parts everything is eternal. Pado ’sya, the place and the living entities are linked with a copula verb because of non-difference between the place and the person residing. Tripadasya is in the singular to express the whole. In the spiritual place (divi) there is eternity situated in his place of three vibhutis…. Beyond the coverings of prakriti (bahih) described by the words trimudha (top of the three gunas), exists the spiritual world described as three parts (trayo padah). The word ca after bahih indicates that sometimes the three parts exist within the material world in places like Mathura. Here are the places (asriamah) of those who do not take birth at all (aprajanam), those liberated from samsara. The places and the inhabitants are eternal, since the previous verse said that the place was without death and sickness. But within prakriti made of the worlds of three gunas (trilokyah) exists the fourth part (aparah), where the karmis live, without being devotees of the Lord (abrihad-vratah). But if they become devotees, then they exist in the other three parts. This verse (SB 2.6.20) explains the Purusha-sukta line tripad-urdhva udait purushah pado ’syehabhavat punah: the three quarters portion of the Lord transcended the material portion; the Lord in the one quarter portion manifested the universe again, as he had done repeatedly before. The smriti also says:

tripad-vibhuter lokas tu asankhyah parikirtitah |
suddha-sattva-mayah sarve brahmananda-sukhahvayah ||
sarve nitya nirvikara heya-raga-vivarjitah |
sarve hiranmayah suddhah koti-surya-sama-prabhah ||
sarve vedamaya divyah kama-krodhadi-varjitah |
narayana-padambhoja-bhakty-eka-rasa-sevinah ||
nirantaram sama-gana-paripurna-sukham sritah |
sarve pancopanishada-svarupaya veda-varcasah || ity adi ||

The spiritual worlds are unlimited in number. They are all suddha-sattva, filled with spiritual bliss, eternal, without change, and devoid of low passions. They are pure gold, shining like millions of suns, personifying Vedic knowledge, filled with pastimes and devoid of lust and anger. These places exclusively serve the lotus feet of Narayana, and are always blissfully singing verses. They are the essence of the Vedas, embodying the five Upanishads.

The word tripad-vibhuti means the spiritual world and pada-vibhuti means the material world. The Sandarbha quotes Padma Purana in this regard:

tripad-vyaptih param dhamni pado syehabhavat punah |
tripad-vibhuter nityam syat anityam padam aisvaram ||
nityam tad-rupam isasya param dhamni sthitam subham |
acyutam sasvatam divyam sada yauvanam asritam ||
nityam sambhogam isvarya sriya bhumya ca samvrittam ||

“The spiritual realm is spread over three parts. One part is this world. The three part spiritual world is eternal. The power of one part is temporary. The eternal form of the Supreme Lord is situated in that glorious place. That form of the Lord is undecaying, eternal, full of pastimes, eternally young, eternally enjoying and surrounded by Sri, Bhumi and Isvari.”.. The jiva attains these two places by specific qualities. He who wanders in the universe is called visvan, the jiva. The jiva wanders on these two paths (sriti). The perfect tense is used to mean the present. These paths are followed to attain enjoyment and liberation (sasananasane). The qualification is mentioned. He who has avidya attains the material realm and he who has vidya attains the spiritual world. However, the spiritual world is actually attained by accepting bhakti after giving up vidya also. Bhaktyaham ekaya grahyah: I am only attained by bhakti. (SB 11.14.21) The Supreme Lord however is the shelter of both paths. He is the shelter of maya who has functions of avidya and vidya. Thus the two paths are dependent on the Lord. This verse (SB 2.6.21) describes the Purusha-sukta line tato visvan vyakramat sasanasanasane ubhe: the jiva traverses the two paths of enjoyment and liberation.”

Also Śrī Jīva Gosvāmī says in his sandarbha that death is the only one quality that makes the material world eka pada vibhuti – tad evam amartyam aiśvaryaṁ tri-pāt, martyam eka-pāt iti tasya catuṣpād-aiśvaryaṁ.

Then the purvapaksa quotes Srimad Bhagavatam 6.16.37
“There are innumerable universes besides this one, and although they are unlimitedly large….”
The universes are not “unlimitedly large”, our brahmanda is 5 billion yojanas diameter + layers.
Again, unlimited is figurative.
The opponent later quotes Brahma Samhita 5.35
“He is an undifferentiated entity as there is no distinction between potency and the possessor thereof. In His work of creation of millions of worlds, His potency remains inseparable. All the universes exist in Him and He is present in His fullness in every one of the atoms that are scattered throughout the universe, at one and the same time. Such is the primeval Lord whom I adore.”
And comments:
“Lord Brahma indicates that each unlimited universe is springing from Lord Krsna, and that each universe is composed of infinite atoms, yet in each atom exists the same unlimitedly potent Govinda from whom more unlimited universes could expand.”
But the purport to this verse corrects his apa-siddhanta:
“..All the mundane universes owe their origin to the transformation of His external potency. Again His abode is beyond human conception; since all worlds, limited and spiritual (cit) exist in Him and He resides simultaneously in His fullness and entirety in all the atoms in all the worlds…”
The “limited” world(s).
The purport ends with stating: “… This argument favors the doctrine of simultaneous inconceivable distinction and nondistinction, and knocks down the contaminating Mayavada and other allied doctrines.”
K.O. knocked out, not O.K.
The title of the article is already self-defeating “.. different sizes of infinity”. Different infinities is impossible. If matter and spirit are both infinite, they will (this is theoretically only) overlap each other, and then there will be one or the same infinity. Infinity is one.

Hare Krishna
Your servant Patita Pavana dasa
Somayaji says :

Jun 30, 2015 at 4:07 pm

In response to Patita Pavana Prabhu’s last comment.

The title asks the question “Are there different sizes of infinity?” and then does a nice job of investigating it. But it seems that the mathematical acumen for an adequate appreciation of the article is beyond the purview of some of the commentators hence they belabor us with a long series of quotations that are meant to defeat a straw-man argument.

In comment http://www.dandavats.com/?p=14199#comment-19885 Shyamasundara Prabhu clearly states the obvious:

“If you did follow the mathematical logic then you would understand that actually they are the same size. Not that one is greater than the other. Why? Because they are “countably infinite” thus you can make a one to one correspondence between them. 1 –> 2, 2–>4, 3–>6, 4–>8, 5–>10,… to infinity.”

So we are wondering why you are going to such great lengths to prove what he has already stated.

You seem to have a negative animus toward the author.

Are there different sizes of infinity?

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