For Yuri; an afterthought to how Dostoyevsky may have replied to Gerard’s objections to the focus on tending to the heart, and his championing of economic development and rationalization of the social world as the primary route leading to the reduction of the world’s problems and, seemingly, the improvement of human nature — in which moral and ascetical practices, such as tending to one’s heart, are seen as superfluous at best. What follows below is not an argument against this (who would begrudge development?), simply an attempt at being an amanuensis of sorts.
Halfway through The Brothers Karamazov, an older gentleman named Mikhail, the interlocutor for the young and newly-pious Zosima, says that “each man [is] guilty before all and for all” (Book VI.2.d), as though all were connected at some root; the “isolation” we now experience is a lie; we have each “separated [our] unit from the whole”. But “Paradise […] is hidden in each one of us” the interlocutor states, and we could enter it tomorrow.
In order to make the world over anew, people themselves must turn onto a different path psychically. Until one has indeed become the brother of all, there will be no brotherhood. no science of self-interest will ever enable people to share their property and their rights among themselves without offense. Each will always think his share too small, and they will keep murmuring, they will envy and destroy one another. 
Presumably, this is because things are connected through their depths, and not through their surfaces, are connected through the wholeness of everything at the root, and not in the isolation of things in the phenomenal (Zosima himself talks about science only having purchase over the sensible world in Book VI); the world is not a machine in TBK, but more like a vast organism, inclusive of both the spiritual and physical. This is why the ocean is used as a metaphor to explain the sensibleness of Zosima’s brother’s having asked the birds for their forgiveness. As Zosima explains it,
all is like an ocean, all flows and connects; touch it in one place and it echoes at the other end of the world. 
The causal pathways in such a world are not mechanical. Madame Khokhlakova at the beginning of Book XI has a swollen foot, allegedly (so she says) because the seminarian careerist Rakitin squeezed her hand too tightly ; like a clown’s balloon dog, squeezing one end allegedly affected the other. One might ask whether illness in TBK sometimes functions in some analogous way.
The ocean metaphor is not temporal, but spatial, but one wonders whether it can be extended temporally. Can causation-over-time also operate in this manner? –did the events surrounding the murder-concealing interlocutor in Book VI (the events regarding the unjust murder of his beloved in his youth, and the whole drama around it when he eventually revealed this), who intimates the oceanic nature of causation, affect the events that unfolded in TBK or the courtroom drama at its end?
The spatial elements of the metaphor certainly imply that two things can be organically connected at a distance. In Book X, the young boy Ilyusha has fallen ill after feeding bread, with a pin in it, to a dog; Ilyusha thinks that the dog has died, as it ran away yelping. Ilyusha’s friend and schoolmate Kolya finds the dog, and nurses Ilyusha back to moral health via the proxy of that same dog. The dog has become a pool, of sorts, a pneumatic connection between the two boys, and affecting the spiritual and moral energy of Ilyusha. At the very end of Book VII, even Zosima and Alyosha are connected across the bounds of death and time. Similarly with Dimitri’s dream at the end of Book IX.8, where the young man Dimitri sees figures who seem to be an infant Dimitri and his mother, appearing in a wasteland, with dried up breasts with no milk.
Oceanic connectedness does not always mean real intimacy. There are times when figures seem to be connected in ways that simply confuse them. In Book IX.6 , the deputy prosecutor says “we asked him [the servant Grigorii] several more times” about when and whether a certain door was open, and the deputy commissioner immediately repeats “I asked him [Grigorii] several more times” regarding inquiry into Grigorii’s testimony — “I” and “we”. There are instance like this throughout the book. This can happen with regard to clothing, too, as with Mitya and Kalganov (also in Book IX — Kalganov being something of a proxy for Mitya in a sense while Grushenka is playing with his hair, even a blurry double of sorts in the narration’s depiction of Kalganov’s characteristic youthfulness and raw innocence, and then being outfitted with Kalganov’s clothes as his own are stripped from him). A confused connection seems to happen in the way that Smerdyakov loves Ivan, only Smerdyakov’s hatred and repulsion effectively drives him to run away from even the one man he loves (prefigured in the song he sings in V.2). In Book V.2, Smerdyakov is strumming on a guitar, and, though he is sitting next to a young dressed-up girl who is doting on him, and though he himself is dressed up, the girl seems merely to be a proxy, and Smerdyakov seems to be singing of Ivan when he lilts
An invincible power
Binds me to my flower 
Ivan and Smerdyakov do seem to be somehow connected: when Smerdyakov tells Ivan to take a train to Moscow (instead of Chermashnya), Ivan is himself amazed that he obeys. Ivan and Smerdyakov have different hearts, however: Smerdyakov can say “I hate all of Russia” , though he seems to hate the character of the nobility even of the nation he considers superior, France (“[w]hen it comes to depravity, […] theirs and ours are no different”). Ivan is full of disgust, but has a basic love for life, as he confesses to his brother Alyosha in Book V.3 ; there is, as it were, a screen separating his mind from his heart (the description of Ivan’s seating arrangement in the very first lines of V.3 describe his mental-emotional situation perfectly in an analogy), and even the Elder Zosima seems to note that Ivan’s heart is in turmoil to resolve a question, and the products of his mind are somewhat disingenuous expressions of the question at play in his heart.  Smerdyakov is as deceived about Ivan as Ivan is about himself, thinking he knew Ivan’s heart, but loving only some ideas emerging from Ivan’s mind, and committing suicide when it became clear that Ivan’s heart was something else, that his real heart was protected by some bubble, his mind like a pustule atop it, and that pustule ready to pop — though, as he killed himself “not to cast blame on anyone” (or some roughly equivalent quote), the attachment to Ivan remained, even as their hearts were estranged. Ivan’s self-neglect lead to a murder and a suicide, and to more besides.
How did it lead to this? Not quite mechanically. Were causality mechanical, then to change the whole would require that one gain control of those political and economic levers of power that hold sway over the largest number of people. Miusov seems to think something like this about changing the world, and himself as a participant in that change (which requires killing others). Rakitin certainly thinks this way about himself (he confesses to Alyosha, at the beginning of the book, in the woods, that people will learn to love humanity in the wake of unbelief in God — though Rakitin seems to hate and despise everyone, and though Alyosha notes to Madame Khokhlakova that Rakitin abuses everyone around him, treating them as beneath him, though hypocritically he expresses hatred towards serf-owners at multiple points). Smerdyakov in V.2 thinks that Russia would have been better off had she been subjected to the discipline of the French. The one who seeks after the levers of power to change the world and relieve injustice may consider that one does it because that one loves humanity, and seeks out such scale of change in a love for humanity; yet an older Zosima, early in the book, says that “those who love people in general are good at hating people in particular.” The contents of Miusov’s and Rakitin’s and Smerdyakov’s hearts, however, shape deeply what these three produce when they acquire a stage, or when they deal with the people about them. Loving particular humans is hard. Yet, in The Brothers Karamazo’s world of oceanic causation, it may be that affecting the whole beneficially is best had –perhaps only really had– via devoted love to the parts one is organically and oceanically connected to. This may be why Alyosha does not try and distance, from the official teachings of the Church, the idea –found in popular Russian Orthodox belief, or folk-belief– of the few solitary monks who can move mountains (see Book III.7 ): it seems that Alyosha finds some truth in it. Perhaps this is because he holds that the solitary ascetic is still connected to everything. We are connected, perhaps, in TBK, not as a massive bundle of discrete points on a Euclidean plane –how Euclid is sidelined in TBK!– but as hearts entwined in some deep root, in an ocean. If so, one makes a start of healing the world by ascesis in the place one lives (the ripples in the ocean of being may move far, even if one is a recluse), by seeking interior purity, and especially by cultivating genuine heartfelt love, rather than gaining access to the levers of power over the exterior features of the social world, as though people were ants.
As an editorial addition, regarding Miusov: he is the one who took in the young Dimitri when Dimitri’s mother had died (Miusov having bonds of affection and relation to Dimitri’s departed mother), and the father dissolved himself in debauchery, and had forgotten all about his son, leaving him to the inadequate care of the servant Grigorii. In some ways, the whole of TBK is an epilogue to the negligences of both Fyodor Karamazov and Miusov, who took him in, and then abandoned the young boy to run off and fight in France. From what we see of Miusov early in the book, he is merely a mirror of Fyodor, even by Fyodor’s own recognition, in certain respects. Certainly, Miusov is very concerned to look like a respected gentleman, and, when he often loses his temper, he is embarrassed about how it will make him appear: his worries about appearing as such-and-such is a barrier between himself and his own heart, and his heart and the hearts of others. It certainly is a barrier between himself and Dimitri, for Miusov needed to abandon this child, whom he was bound to through oceanic ties of organic connection, and run off to a “beautiful faraway” (to steal a line from another Russian writer near Dostoyevsky’s time), to immerse himself in events that he would be able to transmute into a narrative about himself, a carefully curated mask of Enlightenment gentlemanliness.
In neglecting these oceanic ties to Dimitri, and in pursuing these grand mechanical turns in the world, what good motives could there be? Neither Miusov nor Dimitri was helped, and many, many people were harmed by the ripples of Miusov’s denial of his real connections, as he left in pursuit of artificial, mechanical ones.
An afterthought (to a post that is already itself merely an afterthought!) about the origin of this image of the ocean, in Book VI of TBK: the image calls to mind passages from St. Isaac of Nineveh (the Syrian) in his The Second Part, where the ocean is a symbol for several things, whether of the world:
Rig together my impulses for the ship of repentance, so that in it I may exult as I travel over the world’s sea until I reach the haven of your hope. V.14, p.12
Many ships have gone astray in this ocean [of the temporal world?]. For while ears may hear and the mouth may read, they have not tasted the potency of the awareness of this hope [of the aftermath of the lightning flash of mystical joy within the soul] even with the tip of the little finger. XX.21, p.112
or of God’s creative power:
Now, however, with the assistance that comes from grace, let us conclude these matters and approach the riches of (God’s) nature and the ocean of His creative power and the waves and resplendence of his Being. IX.13, p.37
Let us consider then, how rich in its wealth is the ocean of His creative act, and how many created things belong to God, and how in His compassion He carries everything, acting providentially as He guides (creation); and how with a love that cannot be measured He arrived at the establishment of the world and the beginning of creation; and how compassionate God is, and how patient; and how He loves creation, and how He carries it, gently enduring its importunity, the various sins and wickednesses, the terrible blasphemies of demons and evil men. […] X.19, p.43
or of God’s nature or his grace:
the smoothness of the ocean of the peace of His Nature [is not] perturbed by any contrariness on our part. X.23 p.45
how wonderful is the compassion of God! –who can measure the ocean of His grace? XIX.11, p.105
Seeing that His face is set all the time towards forgiveness, by insignificant and tiny means, (so small) they hardly exist, time and time again, by what seem to be chance and unpremeditated occasions, He pours over us (His) immense grace that, like the ocean, knows no measure. XL.13, p.177
or the provision of symbols God offers:
the Divinity dwells inseparably in the Humanity [of Christ], without any end, and for ever; in other words, boundlessly. For this reason we look on the Cross as the place belonging to the Shekhina of the Most High, the Lord’s sanctuary, the ocean of the symbols of God’s economy. XI.24, p.60
or of the interior stillness that comes with the lightning flash of grace from God:
the divine power will cause him [the ascetic] to taste [the exact meaning of the biblical text he is reading, in accordance with the ascetic’s spiritual progress] — that power which acts as a guide to him on the great and extensive ocean of stillness. XXXI.1, p.138
The sea can also be a metaphor for the practice of cultivating interior stillness:
let those who dive into the sea of stillness act as teachers, those who alight on the riches of the sea, (descending to) the heart of the earth. Let us consider as oysters the prayers upon which the intellect alights, the contemplative insights, divine knowledge, wisdom, joy in spirit. XXXIV.5, p.148
It is hardly a surprise that, in TBK, a monk in his cell, or dealing with a small patch of world around and within him or her, tending the earth of his or her heart, can affect the whole world: the legend of the Russian idea of the saint that Smerdyakov suggests, and which Alyosha approves, does more to repair the world, is more “useful”, than a Rakitin who gains a platform in the courtroom and in print, and acquires a wider audience, but whose heart is corrupt.
St. Isaac does not develop this image of the sea into a cosmology — in fact, his physical cosmology is remarkably naive compared to that of the Greek and Latin fathers.  Nonetheless, I cannot help but wonder, given that Dostoyevsky read him, whether this image of the sea, particularly passages about the ocean of God’s creative power and whatnot, or the ocean of this world, did not influence some of what he wrote about causation and relationships.
Fyodor Dostoyevsky, The Brothers Karamazov transl. Pevear & Volokhonsky (New York: Farrar, Straus, and Giroux, 1990) 303
“suddenly once, as he was leaving, he squeezed my hand terribly […] [a]s soon as he squeezed my hand, my foot suddenly started to hurt”. Ibid., 575
Ibid., 230-231, 263
“The earth is as a bed; and the highest heaven as a vault; the second heaven as a wheel adaptated to the higher one. And the borders of heaven and earth are joined one to the other. The Ocean surrounds them as a belt. Beyond it are high mountains ascending unto the sky. The sun goes its way  behind these mountains the whole night. The great sea is beyond them. And this encompasses four times the area of the dry land and one fourth is dry land.” in Mystic Treatises by Isaac of Nineveh: Translated From Bedjan’s Syriac Text with an Introduction and Registers, transl. A.J. Wensinck (Amsterdam: Koninklijke Akademie van Wetenschappen, 1923), 127-128.
Header image is handwritten by Dostoyevsky himself regarding The Brothers Karamazov, and can be found here.