The Makedonian phalanx -- why such depth?

[Paullus Scipio]

Whilst it may be true that Philip learned of Epaminondas' echeloned attacks at Thebes, he does not seem to have used them on this occasion, his first major battle.

Diodorus needs to be read with Frontinus:

Front. Strat. 2.3.2
When Philip, king of the Macedonians, was waging war against the Hyllians (Illyrians), he noticed that the front of the enemy consisted entirely of men picked from the whole army, while their flanks were weaker. Accordingly he placed the stoutest of his own men on the right wing, attacked the enemy's left, and by throwing their whole line into confusion won a complete victory.

It is unlikely, unless echeloned back, that the left stood idle whilst the right attacked.
Frontinus' anecdote, like many of his others, can be seen as a dubious interpretation of the very same sources we have. As we have seen, it was common in Phalanx warfare for the 'elite' unit, whether guards,Agema etc to lead the army on the march, and be on the right wing in battle. Frontinus' "stoutest of his own men" is surely just Diodorus (or his source) "flower of the Macedonians". Frontinus, like Diodorus, has the left wing of the Thracians giving way first ( but doesn't mention the outflanking cavalry). Neither mentions any echeloned or oblique attack, which, had it occurred would surely have been the focus of Frontinus' anecdotal stratagem.

I'm afraid that the way in which you have condensed Polybius' words here is a little misleading. It may not be the case that Polybius has contradicted himself, because the reference to 'close order', and the reference to 16 deep occur in two separate paragraphs, and after describing close order in the first paragraph, in the second one Polybius has reverted to describing what I believe is the 'convention' among Greek authors to refer to depth in 'normal'/open order, and readers would know that such a formation would 'close up' as described in the manuals, and halve it's depth.

I do not think it misleading at all. Your suggestion might be considered pushing the source a little though...

We shall have to agree to differ, I guess. My interpretation at least has the virtue of keeping Polybius uncontradictory and consistent with, I believe, other Greek authors in describing depths in 'normal/open' order, and the manuals. Bear in mind that the Phalanx, Hoplite or Sarissaphoroi, marches and moves in this order all the time off the battlefield and 90% of the time on the battlefield, typically only 'closing up' after the withdrawal through it of skirmishers to it's front for the final charge/advance to contact of 100 metres or so......
Your interpretation would have Polybius completely contradict himself...

Polybios is clearly describing a phalanx “closed up for action” in the first paragraph in chapter and verse. He then illustrates this description via the Homeric quote. Following directly on that he makes it abundantly clear that the charge he is describing is by a phalanx 16 deep:

From this we can easily conceive what is the nature and force of a charge by the whole phalanx when it is sixteen deep.

In other words, from "what I have just described, we can see just how scary and effective is the charge of a 16 deep phalanx".

Clear as a bell.
...absolutely agreed ! D But I postulate that the term "sixteen deep phalanx" means one in 'normal/open' order, 6 ft per man, and that this was a convention used by Greek authors.

Or are you suggesting that Polybios insists the sixteen man pahalnx charges in "open order"?

No, not at all.....I believe, and I think Polybius' Greek readers would know/understand, that a 'sixteen deep' phalanx closed up by means of the rear half-file moving up, so that each man was on a 3 ft frontage, and the phalanx becomes 8 deep, just as Callisthenes says. Similarly, according to Xenophon, a Hoplite battle formation is 4 deep, whereas Hoplites are often described as "8 deep", which is therefore likely also to mean in 'normal/open' order. This hypothesis solves all difficulties and anomalies regarding depths of various phalanxes, and the fact that depths of 8,10 or 12 for Hoplites and 16 or more for Sarissaphoroi are on the face of it, excessively deep. Incidently, I am not the only proponent of this hypothesis - a close examination of Peter Connolly's illustrations of Hoplite drill shows the same 8 deep in open order moving into 4 deep in close order....
Also, you haven't addressed the major difficulty with the idea that 16 deep was in close order that I raised earlier, namely how do they ( the six units of sarissaphoroi, 12,000 strong) get from 16 deep in close order, on a front of a mere 750 yards, to 8 deep on a front of 1500 yards? And this doubling of front, involving troops moving almost half a mile is carried out 'close to the enemy', and must of necessity involve the flanking cavalry and light troops to move sideways, or in echelon perhaps ? This is , I venture to suggest, impossible! This is where actual experience of drilling large numbers of men, or watching mass drill helps! Far more likely that the phalanx expands from 32 deep in open order ( frontage 750 yards), to 16 deep as the rear half moves up from column into line (frontage now 1500 yards), and finally when 'close to the enemy', closes up to 8 deep, on the same frontage, thus not displacing cavalry or light troops and conforming with what we know or can infer of Greek and Hellenistic phalanx drill.