"Please allow me to introduce myself"
I am a man who has been frustrated beyond limit by a litterary style which promises heaven and delivers only headaches!

Can somebody please tell me what codons are?
Here is a not completely humorist report of my attempts to understand Marr's proza.

"The synaptic arrangement of the mossy fibres and the granule cells may
be regarded as a device to represent activity in a collection of mossy fibres
by elements each of which corresponds to a small subset of active mossy
fibres."

I am really surprised the reviewers did not reject this complex sentence as barbaric and obscure! Especially since it does not add anything to the meaning Marr wished to convey.
Let us try to dismember it!

1) The synaptic arrangement of the mossy fibres and the granule cells may be regarded as a device...
2) [this] device represent[s] activity in a collection of mossy fibres by [certain] elements...
3) each of [those elements] corresponds to a small subset of active mossy fibres.

Let us take the expression "a collection of mossy fibres" away since it appears to be redundant.

"The synaptic arrangement of the mossy fibres and the granule cells may be regarded as a device to represent activity by elements each of which corresponds to a small subset of active mossy fibres."

Let us get rid of "elements each of which corresponds to " since it only adds to the confusion, before we change the rest accordingly from singular to plural.

The final result is:

"The synaptic arrangement of the mossy fibres and the granule cells may be regarded as a device to represent activity by small subsets of active mossy fibres."

Obviously "the synaptic arrangement" itself is not a device, but can be analyzed as "small subsets of active mossy fibres". 
Anyway you look at it, it either hides a very deep truth that I am unable to fathom, or a very disappointing triviality: mossy fibers are connected to granule cells.

And that is where the 'codons" get in:
"a codon is a subset of a collection of active mossy fibres." Now we know what all those cryptic sentences meant! It was all to introduce the concept of codon in such a mystifying way that once you found it you had the impression of making a great discovery!

An important specification is:
"The representation of a mossy fibre input by a sample of such subsets is called the codon representation of that input..." 
Wow! Since "a sample of such a subset" is a codon. Marr is actually confirming that "The representation of a mossy fibre input by a codon is called the codon representation of that input..."

Here is an important question: is a "subset" a unity or a set of more than one fiber?

The following precision does not bring any extra clarity:
"a codon cell is a cell which is fired by a codon."
Which would mean:
a codon cell is a cell which is fired by a subset of a collection of active mossy fibres.

To which neurons do these codons refer? When a group of mossy fibers fire what do they reach? Is there a single target, or is it a multitude of targets that then gets the collective appelation of "codon"?

But wait, Marr is not finished:
 "The granule cells will be identified as codon cells, so these two terms will to some extent be interchangeable." 
Until what extent? Does that mean that sometimes they will not be interchangeable?

That still does not answer our question: is each granule cell a codon, or do we need a (sub)set of them to make a codon? 

Oh, I am so sorry, my bad! 
The "codon cell" is the granule cell, not the codon itself, and it is fired by a codon, which is a subset of a collection of active mossy fibers.
What could "fired by" possibly mean? That a whole bunch of mossy fibers target one single granule cell at the same time? That would be then a codon?
That is apparently what is meant by "codon"! Why didn't he just say so?

Noo! That is a pattern! A pattern is formed by all the mossy fibers that connect to a granule cell. This granule cell can be activated by any number of those fibers, and that would be the codon!

Wrong again!  A pattern is formed by all the "active" mossy fibers that connect to a granule cell. And a codon forms a subset of these active cells.
So, in any case, a granule cell contains all possible information about codons? How does it pass on this specific information?
How should I know? I am not there yet!

Marr continues with: 
"The size of codon that can fire a given granule cell depends upon the threshold of that cell". 
This confirms the simple interpretation of a bunch of mossy fibers stimulating a granule cell. The more resistance the latter offers, the more fibers will be needed to surmount that resistance. Makes sense. 

Oh wait, no it does not!
That would mean that the largest pattern takes it all? Or the first one that happens to be strong enough?

"the mossy fibres which synapse with the granule cell determine the codons which may fire that cell."
There is no one-to-one correspondence between codons and granule cells. Many codons can fire the same granule cell. 
But how do the codons know which one of them is allowed to fire the granule cell? Or do they all fire at the same time?

Let us forget about codons and just look at the active fibers that somehow synapse with a granule cell.
According to Marr, not all are allowed to activate the granule cell, even if they are themselves already active.
remember? 
"The size of codon that can fire a given granule cell depends upon the threshold of that cell, [I forgot to add that last time] and may vary..." It is now the granule cell that determines which codons can activate it through its threshold. But even if this threshold can set not only a minimum, but also a maximum, we are back to the rule " the largest possible pattern wins", whatever the concrete situation the neurons are supposed to represent.

Never mind. let us be patient and plod on.
He then comes up with, for me, incomprehensible formulas that are supposed to prove that, somehow, there has been a reduction of patterns from one cell to the other, that is from the mossy fibers to the granule cells. I do not even want to ask if Marr's formulas make any sense to mathematicians, because I honestly do not care! We are talking about the contexts in which movements are taking place. Marr pretends that he is able to express these contexts in mathematical terms that are not derived of an analysis of physical movements in any way, but represent a priori calculations of probabilities. And then he claims that the number of patterns involved has plötzlich diminished? This is pure magic!

Okay! That's it! I give up!