This is a summary of the full dialogue, which you should certainly read first, available at Mind's I, Ch 26
[A dialogue between Achilles and the Tortoise, who likes logic puzzles, and teasing/teaching Achilles]
Tortoise enjoys vinyl records by hanging them on the wall and looking at them. His friend the Alligator slaps them on his belly. Rather than the usual method of slowly extracting the sound a bit at a time with a turntable. Tortoise says the same relations exist between parts and wholes in the music as when they are played on a turntable, and he prefers to take these in visually, all-at-once.
Achilles: That's an odd way to enjoy music.
Tortoise: What if someone told you your way of taking in Leonardo's paintings is odd, they should be enjoyed by listening to them a bit-at-a-time.
All that about different ways to enjoy records was just a preparatory analogy. Tortoise describes a book with a detailed schematic description of Einstein's brain.
[The story deploys a rhetorical device of having Achilles talk about what Tortoise would say, and so on. In this summary, I'll just put such words in T's mouth.]
When neurons in our brains fire, a wave of charge cascades down pathways to other neurons, leaving some chemical traces behind in their wake. The book describes all of this with numbers and abbreviations (what is each neuron's electrical resistance, what is its firing threshold, what other neurons is it connected to, what are the lingering effects after a charge has passed through). The book also describes how acoustical stimulation of the eardrums gets converted into charges in sensory neurons, and how charges in motor neurons get converted into contractions of the vocal cords and the sounds of speech.
Achilles: I wonder what Einstein would have thought about all this.
Tortoise: Why not ask him, using the book?
Achilles: Einstein was a person, not a book. And how can the book respond to an introduction, it's just sitting there.
Tortoise reminds Achilles about the music being stored in the record all-at-once, versus extracting it a bit-at-a-time with a record player. We can convert the sounds "Hullo Dr Einstein. My name is Achilles" using tables in the book into charges in sensory neurons, and trace how those affect other neurons; eventually we'll get to a table giving us the sounds of Einstein's answer---that is, the answer Einstein would have given, if we had stimulated his eardrums in that way before he died. The characters observe that it would take a long time to trace through the book in this way, but agree to pretend it would only take five seconds.
Tortoise: Who would be answering?
Achilles: Just a book, not Einstein.
Tortoise: You could have a whole conversation with the book. How do you suppose he would react, when you told him he wasn't the real Einstein?
Achilles: You're using the pronoun "he" about a process combined with a huge book. That's no "he."
Tortoise: If you addressed him as "Book-of-Einstein's-brain-mechanism" rather than "Dr Einstein," he'd be puzzled. Imagine if you HAD spoken that way to the real Einstein before he died; the book will respond the same way Einstein would have responded.
They explain to the book that he/Einstein died, but his brain was recorded in the book.
Achilles: I'm beginning to be puzzled. Who am I talking to in that book? Is there somebody alive because it exists? Where are those thoughts coming from?
Achilles: How does a book (plus a process) feel?
Achilles: It's sad it would take so long to carry out the conversation. I'd be old before we get very far.
Tortoise: We could record your brain in a second book. In fact we could make many books, and you could have multiple conversations with Einstein at the same time.
Achilles: How am I going to keep track of all those conversations? How would it feel?
Tortoise: Each conversation would be independent of the others. If you asked the books, they'd each only have awareness of their own conversation.
Achilles: Which one would be me?
Tortoise proposes introducing two of the books to each other.
Achilles: Is "I" a person? a process? a structure in my brain? Some uncapturable essence that feels what goes on in my brain?
Tortoise asks: Did Einstein die? or is the book a way to keep him alive?
Achilles: Some part of his spirit was kept alive by the book.
Tortoise: What if no one ever used the book?
Achilles: What made him alive was the process of someone using the book. When he's just sitting there all-at-once, like a record on the wall, he's not experiencing life.
Tortoise: What if the process of using the book went slower and slower?
Achilles: He'd still be alive, my book could keep conversing with him and neither would detect any abnormality if their processes happened at the same speed.
Tortoise: What if it were just one neuron firing every trillion years. What if the clerk in charge of "running" the books skipped out for a drink and forgot to come back? Would it be homicide? You'd still be there, "all-at-once." Was the snail's pace process really much of an advantage?
Tortoise proposes having Achilles being the clerk running a book copy of his own brain.
Achilles proposes they make a machine to run the book.
Achilles gradually becomes persuaded that he'd still be alive so long as the book is intact, even if no one and nothing happens then to be "running" it. The characters discuss what if the book still existed but the instructions how to "run" it were stolen. What if all the main pages of the book were scattered in the wind---would Achilles then still exist, just in a scattered form?
Achilles: What would the poor soul in the book (or me, if that would be me) be feeling?
Achilles decides to go back to the commonsense idea that the only real "I" is the one in his organic brain. That's what feels his emotions.
Tortoise: Isn't the feeling of those emotions just an electrical pattern going through some of the neural pathways in your brain?
Achilles: That sounds wrong, because the book can't feel any neural activity. It could only "feel" its numbers changing.
Tortoise: Couldn't feelings be there all-at-once, just like in records?
Achilles observes that vinyl records don't change as their music is extracted, but minds do, as they interact with the outside world.
Tortoise acknowledges this, but says that minds can continue to experience life even when cut off from the outside world. He compares how the path of a thrown grapefruit can be inherent in the position and velocity of the grapefruit at a single instant, to how a mind that's cut off from the outside might have its future thought evolutions inherent all-at-once in its present structure.
Achilles: I see things more easily in the "bit-at-a-time" picture. Are there any feelings in the "all-at-once" picture?
Tortoise raises a different question. In the "bit-at-a-time" picture, can "you" control what neural pathways your electrochemical waves travel along? Doesn't your neural structure itself determine that?
Tortoise describes A's mind as a labyrinth of rooms. The "hot spot" or "neural flash" of electrochemical activity races through the maze, opening and closing doors. Its passage through some rooms makes vocal cords contract and sound comes out. Sensory input makes the "hot spot" change its path.
Achilles: Normally I think I'm in control of what I think. Your story makes it sound like "I" am just what comes out of all this neural structure; a by-product of lawful physical processes.
Tortoise: What do you mean by "control"? You can't force your "neural flash" to deviate from the path of least resistance, but the Achilles of one moment is affecting what will be the path of least resistance in the next.
Achilles: But then I can't think whatever I want, but only what an earlier version of me set me up to think.
Tortoise: But that IS what you want to think about.
Achilles: I wonder if I could learn enough about my neural structure to predict what my "neural flash" would do before it got there.
Tortoise: Wild paradox! The very act of learning about yourself would change you, so now you'd have to learn about those changes, and so on…
Achilles: So my mind can't understand all of itself, only at best all of how it used to be.
Tortoise: Do thoughts occur in the mind or in the brain?
The characters discuss analogies between the word "mind" and the word "beauty"---beauty isn't locatable in space, but instead is a structural feature of some complex things. Is there any such "entity" or Thing-with-a-capital-T as beauty? The analogy to "minds" is left mostly implicit.
They return to A's question of where is the "real me"?
Achilles: I'm not sure where it is. I could say "The real me is here now," but the book could say this too. I could say "I know I exist, I feel it." But so too could the book. Maybe these "feelings" are just an illusion.
Achilles remembers the idea of several copies of the Achilles book having conversations with multiple people at the same time.
Achilles: Each book would be programmed to say "I am the real me, I am feeling my own emotions, and anyone else who claims to be Achilles is a fraud."