Edit 5: Death of Socrates

[Lizzie]

I'll offer some thoughts at this point. I appreciate how you've simplified it from the last version -- it's not as sprawling. I certainly agree with you that you were trying to cram way too many concepts into one piece.

As I understand, this genre of poetry doesn't have many hard and fast rules. You can talk about what you see in the picture or it can be generally inspired by the piece on whatever level you choose.

I think the two pitfalls you need to avoid are (1) being overly descriptive of the painting (it comes across as just prose and rather redundant since the reader can see for themselves) and (2) sounding too much like a philosophy textbook. This version seems to be better on both fronts, so

A couple of line by line notes:

Death of Socrates

After Jacques-Louis David's "The Death of Socrates", 1787, oil on canvas

Indifferent fingers hover towards -- hovering is lingering near an object, unmoving or moving very little. "Toward" makes no sense to me here.
death- swilling in a copper cup,
offered by the crimson executioner.

This room contains a burn pile 
of autumn leaves started by a match 
stricken on opinion that set aflame
the students' doubts;
meditation didn't burn.

Old man, you sit where you shouldn't -- I like the voice here and in the next stanza, where the subjects of the painting are directly addressed. Having a conversation with the people in the picture is more engaging than musing to yourself about the painting. I'd use this voice throughout, if I were you.
and old, you shouldn't be. Unless -- There are a few things I don't like about this sentence structure. Primarily I object to the inversion of "you shouldn't be" instead of saying 'you shouldn't be old' which reads more naturally. Also, I don't like the repetition of old and shouldn't. Ending on the verb is also awkward. I don't think you can justify starting a sentence with "unless" since that means that this beginning sentence has no verb.
an echo of stories in your absence
reified in detail all around you,
down to the arrows on the sleeve
of a swooning cohort- contradicting -- there's no need for a hyphen...a comma will suffice after cohort, unless you're joining cohort and contradicting into one word. A hyphen is a different grammatical tool than the em dash. An em dash has the effect of setting off a phrase like parentheses.
what you taught of Form and how -- weak line break. The beginning and ending words of a line receive special emphasis, and there's no reason to highlight "how" here. I'd merge the fragment below with this line.
things appear.

In contrast to your teacher,
the apotheosis of your beliefs 
is a bitter one. -- I like the comparison of bitterness with the presumed taste of the poison.

Edit 1: Death of Socrates
 
I guess Asclepius is owed a cock, 
        whatever that means. 
The philosopher who said it 
said it as he pointed up,
explaining how we can be unaware
because our souls forget things like
an apple's sopping crunch, to Crito-- 
who is tugging at his pendent thigh. 
 
His other leg is placed upon  
the makeshift lectern of a mattress, 
protruding from his drapery 
like morning light would mutely break 
through dusty curtains onto bed, 
glowing like his chest. 
 
Being sure enough 
that hemlock washes down like wine 
will get the executioner, 
who couldn't even bear to watch, 
demoted to the job of cupbearer 
and death to getting blackout drunk. 
I would love to be that sure. 
 
In this final lecture, 
the apotheosis of opinion 
seemed to overwhelm Apollodorus,  
who left the room and grinds his brow 
against stone, and his swooning students, 
who curl and twist 
like autumn leaves in a burn pile. 
 
Except for one 
who seemed older than he should've been, 
and wasn't dressed in autumn colors, 
and shouldn't be where he is seated- 
unless stories of his teacher's death 
reified behind his head
every imagined detail down
to the needlework of arrows  
on a student's sleeves,
real enough to contradict
what he taught of Form and how
things appear.
 
I bet he knew just what his teacher meant  
about some roosters being owed 
in the moment that he bowed his head 
to let his eyelids rest beneath reflective shades; 
I'll get around to googling
his teacher's final words.

Original: Death of Socrates

I guess Asclepius is owed a cock, 
        whatever that means. 
The philosopher who said it,
said it with a finger propped
on how we can be green because
our souls forget things like
an apple's sopping crunch, to Crito-- 
who is clinging to his pendent thigh. 
 
His other leg is placed upon
the makeshift lectern of a mattress,
protruding from his drapery
like morning light would mutely break
through dusty curtains into bed,
glowing like his chest.
 
I envy just how sure he is; 
reaching for the hemlock 
as if it was a glass of wine, 
as if the executioner  
was nothing but a cupbearer 
who cannot even bear to watch 
and death was just a drunken dream. 
 
In this final lecture,
the apotheosis of opinion
seemed too much for Apollodorus,  
who grinds his brow
against stone, Xanthippe,
who grieves just past the hall,
and his swooning students,
who curl and twist
like autumn leaves in a burn pile.
 
Except for one 
who seems a little older, 
and isn't dressed in autumn colors, 
and shouldn't be where he is seated--
unless the stories of his master's death 
manifested into strapping colors 
strong enough to lift their limbs 
from the canvas, contradicting 
his teachings of ideal and phenomena. 
 
The man was Plato, and I bet he knew 
what his teacher meant  
by owing some medicine god a cock 
when his spine was tied to 
a dumbbell of decrepitude. 
I'll know too 
--right now, I don't-- 
nor would I intend to.

Overall, I think it's going in the right direction. You might also try writing it in meter or with a rhyme scheme to reinforce that it's poetry not prose.

I like that you're trying out different styles. It's always a good thing to push yourself in new directions as a writer.

Best to you,

Lizzie