Clumps and Chumps (or why film isn't binary)

There has been much talk on the internet about how many pixels it takes to out resolve film, the answer is 'it depends'
Many 'experts' have put their point of view across, some are disastrously wrong, certainly on a factual level.
here is one such assertion from Michael Reichmann:
Clumps and Chumps

"A very fine-grain film has grain particles that are about 2 microns in size. A typical DSLR has individual pixels that are about 6 microns in size. Ergo, film should outresolve digital. Right?
Not so fast! Here's the catch that many testers trip over. Grain particles are binary. An individual film grain can only be either black or not-black, on or off, exposed or not exposed. Sort of a binary device. A photo site (pixel), on the other hand, has a range of thousands of brightness levels, because it's an analog device. (Curious isn't it, that at this level film is binary and digital is analog?)
What this means is that it takes a clump of between 30-40 grains of film to represent a full tonal range, (similar in concept to the dithering done by inkjet printers to produce continious tones), while on a sensor each individual pixel can reproduce from hundreds to thousands of tonal levels."

Now for some facts.
Film emulsions are generally Ag/Br/I atoms combined into crystals from about 1 - 10 microns in size which are stacked in layers and dispersed randomly throughout the emulsion. They contain millions of atoms and many sensitivity specks which consist of sulfur and gold.
When film develops, it can form anywhere from 3 silver metal atoms minimum up to the entire grain, and grains can be stacked, and therefore the dynamic range of density is analogue in nature and virtually infinite. For practical purposes, it ranges from 0.1 - 3.0 density units in a normal negative B&W film.
Still need convincing?
Here's what's wrong with Michael Reichmanns essay.
Film grains are not binary, not even close they actually are made up of millions of silver particles that when looked at closely resemble a wire wool pad, the more photons of light that strike the grain the denser the filamentary structure becomes and the amount of light passed by that structure varies, the structure also develops randomly.

How Film Works:
Before exposure the structure of each grain consists of Ag+Br (silver bromide) atoms and sensitivity specs (sulphur and gold) the Ag atoms are positively charged (missing an electron) which is how they are bonded to the bromide atom.
When a photon of light strikes the silver atom they lose their positive charge and separate from the bromide atom, they are now silver ions and move (within the grain) towards the sulphur 'sensitivity' specks to form a filamentary structure, the more silver ions the denser the structure.
During development these structures are converted into metallic silver which is black, the bromide atoms are absorbed into the developer, fixing removes the silver atoms that weren't struck by any photons, leaving that part of the grain clear.
Here is an image (45,000x magnification) clearly showing the filaments and 'wire wool' like structure of the developed grain:


The image above pretty much nails the lie that film is binary or as Michael Reichmann put it:-
'An individual film grain can only be either black or not-black, on or off, exposed or not exposed'.

The film grain in the above picture shows that grain can be both black and clear at the same time as well as each filament differing in density, filamentary in varying degrees, letting different amounts of light pass though the grains themselves, being stacked up to 10 layers deep to give different tones.

Hardly the description of something that can have only 2 states, as would be the case if they were binary.

In his book 'The Fundamentals of Photography' C.E.K Mees states:
"Any silver deposit in the negative will let through a certain proportion of the light which falls upon it. A very light deposit may let through half the light, a dense deposit one-tenth, a very dense deposit one-hundredth or even
only one- thousandth".
I think Mr Reichmannn has made the common mistake of confusing the silver atoms that move towards the sensitivity specs with the grains themselves, coupled with not realizing that those grains are not opaque that and according to all the text books even the darkest grain will pass some light.
An easy mistake to make, I just wish his post was less 'pithy' especially considering his quite considerable errors, but I'll give him the benefit of the doubt and suggest a little research.
Here is a list of the books and references I have used for this article:

The Theory of the Photographic Process– C.E.K Mees and T.H James

The Fundamentals of Photography C.E.K Mees

The Science of Photography– H. Baines
Kodak Technical Document H1
Advice and help from Kodak research Europe (many thanks guys)
Information and help with writing this article Ron Mowrey

Here's a link to a paper by Nestor Rodriguez (Senior Technical Associate at Eastman Kodak):
Color 35mm film questions
Quote:
Q: What are the main differences between the way images are recorded on film and digital, aside from resolution?

A: "Film is analog, like the human eye. It sees and records continuous tonal gradations between black and white.

Edit: I have been asked to mention by a photographic engineer that the clumps and chumps article focuses on monochome film in order to make a more 'black and white' argument. It needs to be stressed colour film works in a similar way to mono initially but has a least three colour records, with the grains in each record being removed leaving a dye cloud which varies in size and density depending on the amount of photons that hit the parent grain. So in colour film grains (or rather dye clouds) vary in density (as in mono film) and also colour depending on the record they are contained in, not something that fits the 'on/off switch mentality of the 'clumps' argument.

Its difficult to argue from any perspective that the above (focussed on the cyan layer of a slide film) is or can be represented by a 0 or 1 value. Doubters should note the different densities, sizes and distribution of the dye clouds in a 3D stack.