1. "Walking the floor of the deepest ocean" is from a saying by Yueshan Weiyan (745-828):  "We should stand atop the highest mountain, walk the floor of the deepest ocean." 

"What are you thinking?' (literally, "what mental act is is this?") is a standard Zen retort to an inadequate statement.  "Passing through the barriers and breaking down the sections" refers to successful Zen practice.

The translation obscures Dôgen's play in this paragraph with the graph gyô, rendered variously here as "practice," "walking," "goes," and "thinking."
 
2.  The entire passage here is from the Recorded Sayings of Mazu.  The first quotation represents Mazu's (slightly abbreviated) quote of the Vimalakirti Sutra, in which Vimalakirti is instructing Mañjushrî on how a sick bodhisattva should regard his body.  The second quotation is Mazu's comment, in which he goes on to say that the samadhi collects all the dharmas as the ocean collects the water of all the rivers. 

The awkward translation "thought moment" tries to preserve something of the ambiguity of the term nen, used in reference both to moments of time and individual mental events.  The term will reappear below in both senses.
 
3.  "Original" and "initial enlightenment" are terms widely used in East Asian Buddhism to distinguish respectively the bodhi inherent in the buddha nature and the bodhi attained at the end of the bodhisattva path.
 
4.  Some versions of the text, especially in the sixty-fascicle redaction, do not repeat the quotation here.
 
5.  The last sentence here is generally understood to mean that, in the higher "encounter" with "dharmas arising," the "encounter" between self and other, subject and object, is transcended.  The obscure preceding phrase, "never leaves behind arising," is usually interpreted to mean that each instance of arising is complete in itself and does not leave behind some arisen "thing" that could be the object of knowledge.
 
6. The "twelve times" are the twenty-four hours of the day, figured traditionally in two-hour divisions; the "three realms" are the realms of desire (kâma), form (rûpa), and formlessness (ârûpya) that together make up existence in samsara. 

"Skin, flesh, bones, and marrow" is a standard Zen expression, much used by Dôgen, for the entirety, or complete truth, of something; from the responses of Bodhidharma to his four disciples, "You have got my skin", etc. 

In his distinction between a "statement" and a "saying" here, Dôgen seems to be saying that, though it is not stated, "I arise" can be be a significant saying.  The argument here is probably playing with the sense of arising alluded to in the remark, "it should be 'arisen!'" which is taken from a saying of Caoshan Benji (840-901):

[A monk] asked, "There's a saying handed down from the ancients, 'No one who has fallen to the earth can arise without depending on the earth.'  What is this 'falling'?"
The master said, "Consent to it."
[The monk] said, "What is 'arising'?"
The master said, "Arisen!"

This passage occurs in the Jingde chuandeng lu just before Caoshan's teaching on the ocean that Dôgen will cite below.

For one possible interpretation of the argument of this discussion of "arising," see Supplemental Note 1.

7.  From the famous Lotus Sutra parable of the burning house.  Notice that Dôgen is here using the expression "an old buddha," usually indicating a previous Zen master, for the Buddha Shakyamuni.
 
8.  From Loshan Daoxian:  "Loshan asked Yantou, 'When arising and ceasing don't stop, what's it like?'  Yantou said, 'Who's arising and ceasing?'"
 
9.  See above, note 8, for the expression "who's arising and ceasing?"  The three phrases beginning with "those who can attain deliverance through this body" are from the Avalokiteshvara chapter of the Lotus Sutra, in which it said that, to those who can attain deliverance through contact with a particular body (a buddha, a pratyekabuddha, a shrâvaka, etc.), the bodhisattva Avalokiteshvara appears as that body and preaches the dharma for them.

"The past mind cannot be got" is from the Diamond Sutra.  "You've got my marrow," "you've got my bones," are from Bodhidharma's comment to his disciples, mentioned above, note 6.

For an interpretation of this passage, see Supplemental Note 2.
 
10. This passage reflects a conversation, much treasured by Dôgen, between the Sixth Ancestor, Huineng, and his disciple Nanyue Huairang.  Here is the version of the story given in Dôgen's Shôbôgenzô sanbyaku soku.

The Zen Master Dahui of Mt. Nanyue visited the Sixth Ancestor.  The Ancestor asked him, "Where do you come from?"
The Master said, I come from the National Teacher An on Mt. Song."
The Ancestor said, "What is it that comes like this?"
The Master was without means [to answer].  After attending [the Ancestor] for eight years, he finally recognized the question.  Thereupon, he announced to the Ancestor, "I've understood what you put to me when I first came:  'What is it that comes like this?'" 
The Ancestor asked, "How do you understand it?"
The Master replied, "To say it's like anything wouldn't hit it."
The Ancestor said, "Then is it contingent on practice and verification?"
The Master answered, "Practice and verification are not nonexistent; they're not to be defiled."
The Ancestor said, "Just this 'not defiled' is what the buddhas bear in mind.  You're also like this, I'm also like this, and all the ancestors of the Western Heavens [i. e., India] are also like this."

The "adventitious defilements" (Sanskrit âgantuka-klesha) are the spiritual defilements understood as extrinsic to the mind.  The argument here probably hinges on the multivalent term dharma.  While the dharmas (i.e., phenomena) may be both defiled and undefiled, the dharmas (i.e., the truths) taught by the Buddha are always pure.  The "ceasing" of the dharmas in this latter sense is the truth that all dharmas in the former sense are "empty" of inherent existence. 
 
11.  This obscure final sentence is subject to various interpretations.  Some would take it to mean that, while both the arising and ceasing of the self are beyond what can be stated, they are not the same.  Others would see the second clause as a reminder that "ceasing" here is not the same as death. 

The expression "so many hands and eyes" is an allusion to the thousand-armed Avolokiteshvara, who has an eye in each of the hands.  Although here we may take the passage to mean simply that "ceasing" can be understood in many ways, the allusion to Avolokiteshvara's hands and eyes introduces material that Dôgen will develop below, from a dialogue between Yunyan Tansheng (780?-841) and fellow disciple Daowu Yuanzhi (769-835).

Yunyan asked Daowu, "How does the bodhisattva of great compassion use so  many hands and eyes?"
Wu said, "Like a person searching behind him for his pillow in the night."
Yan said, "I understand.  I understand."
Wu said, "What do you understand?"
Yan said, "The entire body is hands and eyes."
Wu said, "You talk big talk, but what you say is eight or nine tenths."
Yan said, "How about my fellow teacher?"
Wu said, "Throughout the body hands and eyes."

The four phrases beginning with "unsurpassed great nirvana" are probably after a verse by Huineng (though the source of Dôgen's substitution in the last line is not clear):

The unsurpassed great nirvana,
Perfect and bright, always quietly shining.
The commoners call it death,
The other ways take it as annihilation,
Those who seek the two vehicles
Treat it as the unconditioned.

12.  See above, note 11, for the allusions here.  The "four great [elements] and five aggregates" refer respectively to the four primary forms of matter (mahâbhûta), earth, water, fire, and air, of which the physical world is composed, and the five "heaps" (skandha) into which the psycho-physical organism can be analyzed.
 
13.  Dôgen is here again alluding to the dialogue between Huineng and Huairang cited above, note 10. The odd locution, "this is," here is a play with the passage of Mazu cited earlier:  "This is called the the ocean seal samadhi."

The expressions, "officially, you can't insert a needle; privately, you could drive a horse and cart and through it," and "in meeting, he doesn't bring it out; but if you raise the point, he knows it's there," are popular sayings in Zen literature.  Both seem to be used here to mean something like, "on the surface, not obvious, but nevertheless true."

See Supplemental Note 3 for an interpretation of the argument of the text on "ceasing."
 
14.  Dôgen is alluding here to a poem by the Tang master Chuanzi ("the boatman") Decheng  (dates unknown):

A line of a thousand feet goes straight down.
The slightest motion of a single wave, and ten thousand waves follow.
The evening is still, the water cold; the fish aren't feeding.
I come home with a fully empty boat, loaded with moonlight.

The "hand groping for the pillow" at the opening of this paragraph is from the conversation, cited above, note 11, on the thousand-armed Avalokiteshvara.  The paragraph then intertwines two passages from the Lotus Sutra.  (1) From the Sadâparibhûta chapter: "After hundreds of millions of tens of thousands of kalpas, after an inconceivable period, they [the bodhisattvas] can hear this Lotus Sutra.  After hundreds of millions of tens of thousands of kalpas, after an inconceivable period, the buddhas, the bhagavats, preach this sutra."  (2) From the Devadatta chapter:  "In the ocean, I always preached only the Lotus Sutra of the Wondrous Dharma."
 
15.  The awkward translations "former face," "latter face," "former head," "latter head" struggle to preserve the play here on the colloquiual Chinese suffixes mien and tou.  Though they would ordinarily function simply as nominalizers, Dôgen uses their primary semantic senses to move from former and latter "faces" to the "face" (i.e., surface) of the ocean, then from former and latter "heads" to the common Zen expression "putting a head on top of your head" (i.e., adding something superfluous).
 
16.  Dôgen is here invoking the so-called "three seals" of Zen:  sky, water, and mud (sometimes interpreted respectively as the dharma, recompense, and transformation bodies of the buddha).  The translation "sealing sky" loses the metaphysical connotation of the term inkû, which could also be rendered "sealing emptiness."  The "mind seal" is of course a favored metaphor for the authentification of the transmission of the awakened mind from master to disciple.

The expression "getting drenched" probably invokes the Chinese idiom "muddied and drenched," used as a metaphor for immersion in complicated affairs or language.

This paragraph introduces several phrases from the poem Caoan ge, by Shitou Xiqian (700-790):

The person dwelling in his hermitage remains forever,
Not belonging to the center, the inside or outside.
He doesn't dwell where the worldly dwell;
He doesn't love what the wordly love . . . .
He's not in north or south, east or west . . . .
Turning the light and shining it back, he immediately comes back home.

(Notice that Dôgen's version has substituted "what is loved by the sages" for Shitou's "the worldly.")

See Supplemental Note 4 for a possible interpretation of this passage.
 
17.  From the Caoshan chapter of the Jingde chuandenglu.   Great Master Yuanzheng of Caoshan is Caoshan Benji (840-901), disciple of Dongshan.  The translation of the last line is tentative.  In his quotation here (as in his Sanbyaku soku), Dôgen has cut off the last three graphs of the original text, making the syntax of the final sentence difficult to parse.  (The original would read something like, "The ten thousand things are not its merit; stopping the breath has its virtue.")

The notion that "the great ocean does not house a dead body" is a fairly common one in Buddhist literature.  It occurs, for example, in the Dazhidu lun, where it is said that those who break the monastic rule cannot remain in the sangha, just as the waters of the ocean do not house a dead body.
 
18.  "Yunju" refers to Yunju Daoying (d. 902), another disciple of Dongshan.
 
19.  The "inner ocean," "outer ocean," and "eight oceans" refer to the eight oceans surrounding Mount Sumeru in Buddhist cosmology, of which the first is called the inner and the remainder, the outer oceans.  The "water  of the eight virtues" refers to the excellent water in the oceans surrounding Mount Sumeru (and filling the lakes of the Pure Land of Sukhâvatî).  It is said to be sweet, cool, soft, light, pure, oderless, harmless to the throat, and harmless to the stomach.
 
20.  A series of allusions to Zen literature:  "When the dark one comes . . . ." is a tentative translation for a notoriously obscure saying of Puhua, recorded in the Linji lu; "dead ashes" is a common expression, used in both positive and perjoratives senses, for the mind in trance, as in the idiom "dried wood and dead ashes";  "encountering how many springs, with core unchanged" is from a verse by Damei Fachang (752-839):  "Broken dead wood keeping to the cold forest / how many springs has it met without changing its core?"
 
21.  "Duofu's one grove of bamboo" refers to the following dialogue found in several sources:

A monk asked, "What is Duofu's one grove of bamboo?"
The master answered, "One or two stalks are slanted."
The monk said, "I don't understand."
The master said, "Three or four stalks are bent."

22.  "It will only take ten thousand years" alludes to the answer by Shishuang (807-888) to the question, "How about when one threads a single string through many holes?" "This old monk makes one move" uses a metaphor drawn from board games; the translation loses the pun on the term chaku, used here both for "belonging" and "placing" (a piece on the board).

For the expression, "what are you thinking?" see above, note 1.  "I've always had my doubts about this guy" is a remark by Linji in response to the saying by Puhua quoted above, note 20.