How continuous was combat?

[Patrick Waterson]

The discontinualists place the issue of human endurance centrally and assume that human endurance then can be compared to human endurance now.

Nicely encapsulated.  On the subject of human endurance generally, is anyone familiar with early 20th century shipbuilding and in particular how long riveters could or would keep up the process of hammering home one red-hot rivet after another with quick, precise strokes of a weighty hammer?

Take a look here and see how long you think they kept it up.

All we can do is attempt a reasonable theory.  And all these discussions can do is explore the field, throw up ideas and let members form their theories.

They can also air evidence: not everything is pure theory.  On which point ...

It has all been unfocused but I think we know that what we are talking about is the dynamic standoff model of Roman infantry combat, and it might have been better to stick to that more closely.

Better late than never.  Anyone care to outline the basics of this model and any source evidence they can find to support it?

... a computer simulation can't tell you what actually happened. What it can do is tell you whether your conceptual model looks and feels plausible when you see it in action, and also whether, when given inputs as close as you can make them to what the sources describe, it produces outputs close enough to be satisfactory to what the sources describe.

Eminently sensible.

Re: Roy's thoughts - manual toy solider (or cardboard) wargames have too much abstraction (rightly, if they are to be games) to be useful as combat models (IMHO) - though they might (Lost Battles) be useful as battle models. Whether losses are tracked as cohesion, fatigue, or casualties doesn't really make much difference - different words for the same thing (in model terms, not in real life terms - ie gradual unit degradation). Agree very much about player choices - I would love to see wargames where players still had something to do, decisions to take, once units are in combat, rather than just rolling dice, adding factors or checking tables.

Hear, hear.

[Erpingham]

They can also air evidence: not everything is pure theory.

Explore the field/air the evidence - similar idea really.  Pure theory hasn't played a part on either side of this debate as far as I can see.  All parties are using their theories to explain the observed evidence.  What we could do with is more solid statement of these theories, which would reduce misunderstanding and allow us to see the elephant(s).

[aligern]

My grandfather worked as a riveter...I think he marked up plates. He certainly worked at Austinband Pickersgills in Sunderland.  He died before my time,though. There is quite a bit of rest built into the riveting process, because each rivet has to arrive and be fitted in the hole fresh from the furnace and then the man blocking the rivet takes position and the riveter uses the pneumatic hammer. So there is a little bit of recovery time built in and then a bit more as a new plate is moved into place. We might be better placed to look at how coal was cut at the face by hand or how loggers work,nthough for bith those jobs there are pauses, for the collier when enough is cut to fill a basket and for the lumberjack, when the log or trunk s cut through.
Of course rivets and trees do not hit back so the men concerned do hot have to bear blows as well as deliver them.
Roy

[Patrick Waterson]

Except it did not work quite like that: the plates were already positioned and attached with a few bolts through holes near the corners by the time the riveters got to them.  Once the majority of the rivets were in place the bolts came out before the riveters reached that part of the plate.

Rivet arrival was quite rapid: they were thrown from the furnace (with tongs) and caught in something resembling a small one-handed coal bucket, from which they were promptly extracted (with tongs) and passed to the holder-upper, who thrust them through and held them there for the riveter (who took five years to train, about the length if time it took to build a battleship in the 1930s) to do his stuff - or their stuff, as they often worked in pairs to get a better shape on the rivet head.

Forgive the trip down memory lane.  We may agree that professions do not necessarily provide the best comparison with soldiering, so here is a little something from Ammianus.

First, a skirmish with the Persian van.

"Our soldiers, inflamed by this sight, since only a small stream separated them from the enemy, were in haste to attack them, but the emperor restrained them; however, a fierce fight took place not far from our very rampart between our outposts and those of the Persians, in which Machameus, general of one of our battalions, fell. His brother Maurus, later a general in Phoenicia, tried to protect him, and after cutting down the man who had killed his brother, he terrified all who came in his way, and although he was himself partly disabled by an arrow through his shoulder, by main strength he succeeded in bringing off Machameus, already pale with approaching death, from the fray.

And when, because of the almost unendurable heat and the repeated attacks, both sides were growing weary, finally the enemy's troops were utterly routed and fled in all directions. As we withdrew from the spot, the Saracens followed us for some distance but were forced to retreat through fear of our infantry; a little later they joined with the main body of the Persians and attacked with greater safety, hoping to carry off the Romans' baggage; but on seeing the emperor they returned to the cavalry held in reserve." - Rerum Gestarum XXV.1.2-3

We note the character of the fighting, with 'repeated attacks' and fierce local combats, both sides growing weary as a result.  A not dissimilar action took place the following day against the Roman rear.  The day after that, the main Persian army came up.  Now we shall see Ammianus describe a full-scale engagement, i.e. a battle.

"Although these sights caused no little fear, the emperor, guarded by troops of armed men and with his trustworthy generals, full of confidence, as the great and dangerous power of the enemy demanded, drew up his soldiers in the form of a crescent with curving wings to meet the enemy.

[17] And in order that the onset of the bowmen might not throw our ranks into confusion, he advanced at a swift pace, and so ruined the effectiveness of the arrows.  Then the usual signal for battle was given, and the Roman infantry in close order with mighty effort drove the serried ranks of the enemy before them.

[18] And in the heat of the combat that followed, the clash of shields, the shouts of the men, and the doleful sound of the whirring arrows continued without intermission. The plains were covered with blood and dead bodies, but the Persian losses were greater; for they often lacked endurance in battle and could with difficulty maintain a close contest man to man, since they were accustomed to fight bravely at long range, but if they perceived that their forces were giving way, as they retreated they would shoot their arrows back like a shower of rain and keep the enemy from a bold pursuit. So by the weight of great strength the Parthians were driven back, and when the signal for retreat was given in the usual manner, our soldiers, long wearied by the fiery course of the sun, returned to their tents, encouraged to dare greater deeds of valour in the future." - idem XXV.1.16-18

Here there is no break in the action, the army fighting as a coordinated whole and driving the foe off the field by 'the weight of great strength' (pondere magnarum virium).

The above two extracts demonstrate the difference in treatment between a skirmish - an intermittent action, one in which attacks are repeated and intervals in the combat are thus presumably present - and a general action (battle) in which no breaks in the continuity of the action are mentioned or even implied - quite the reverse, in fact: he specifically excludes any intermissions.

[Dangun]

I think continuity may be too much for a single step.

Maybe we should start by collecting and identifying evidence for duration first.
(It seems safer to interpolate continuity from duration, than it does to extrapolate continuity from a model of practical endurance.)

Next I'd suggest that collecting evidence for casualties gives us casualties per unit of duration and some useful inferences concerning continuity.

Lastly (I guess there might be some miracle quotes on endurance out there, but short of finding them...), rather than leap to analogies like boxing or riveting, wouldn't it make more sense to use out of period data. While musketry sources might not do much for us, there is probably some useful stuff on duration, casualties, endurance and continuity lying in the out of period cavalry and melee descriptions.

[aligern]

Riveters took five years to train because the shipyards were riven with restrictive practice and you could only get the better jobs by awaiting your turn. The whole farrago fell apart when competitors entered the market with new techniques and no restrictive practices.
However, to Patrick's examples from Ammianus, the first does as Patrick  concedes sound susceptible to punctuated fighting, with repeated attacks.  However, as I said earlier I am very open to there being more happening on the battlefield than simply two lines meeting, with units moving,breinforcing, covering and replacing, so, as I think Patrick concedes, the nature of the combat might enforce breaks.
The second example is skewed because the Persians do not stand up to the Roman attack. The Romans are not exhausted becaipyse the Persians fall back and are such poor hand to hand fighters that they do not deter the Romans. Interestingly, though the Persians shoot as they retreat. Given that it would be exceedingly difficult to shoot at close range  at ranks of the enemy that were engaged with your own front ranks is it possible that the Persians are breaking off far enough back to engage in bowfire before the Romans come on again.
Of course there is the potential problem that the author's description is both linear and comprehensive so the battle is described as a unity whereas in reality there are different actions going on at the same time and the author is giving a partial and higlighted account with only elements of each action included to give colour to his main point, that Persians do not like true Roman cold steel. What happened to the Romans javelins ? What to the vaunted darts? Were they thrown or dropped? Are some of the Persians cavalry?    Ammianus description looks a bit like a raft of topoi...they came on in the same old way and we saw them off in the same old way😉
Roy

[RichT]

Fascinating though the riveting digression is (riveting, you might say), it is a red herring, as you are not comparing like with like. Methodically bashing a rivet is not the same as fighting someone who is simultaneously trying to kill you.

The last few posts show why this thread has gone nowhere and likely will go nowhere. We have collected some comparative durations (Medieval ones) - but the problem with them, as with ancient battles, is deciding what we are we measuring the duration of. That a battle might last hours does not prove that any individual man was standing fighting non stop for hours. We can't ever tell for sure, when a source says that the fighting continued for hours (or minutes or whatever it might be), whether this means there was fighting going on (somewhere) for hours, or whether every individual in the front rank was fighting for hours. The former seems obvious to me, both a priori and through comparison with other periods, but if someone is going to insist that it means continuous fighting for every individual, it is going to be hard to prove him wrong.

The most recent batch of Ammianus quotes are a case in point. For a start, the pitched battle, as Roy says, sounds to me like a perfect example of non-continuous combat - giving way, shooting, enemy prevented from pursuing. Then the emboldened sentence, "the clash of shields, the shouts of the men, and the doleful sound of the whirring arrows continued without intermission" just does not prove that every individual front rank man was doing all this continuously for any given length of time (let alone hours) - just that this was happening somewhere on the field all the time. Again, this is why these discussions make no progress and end up frustrating more than enlightening. We are reading the same texts and understanding them in completely different ways. The battle descriptions we have are extremely terse, high level overviews picking out a few key details of vast complex dynamic battles involving tens of thousands of men. Extracting a sentence from such a high level description and insisting it is a complete and detailed account of everything that happened in that battle seems to me self evidently daft - but again, I can't prove it in a way that would silence all contrary opinions.

To go back a moment to my modelling suggestion - if a dynamic model assumes formations (small units) stood in contact for hours fighting then there will be implications for how battles work - things like outflanking movements, use of reserves etc will be affected in ways that are not obvious just from sitting with furrowed brow imagining it all. Likewise if fights are short and units tire quickly. This is how such a model could help. Gettysburg, the game (and for an abundance of clarity, I'm not suggesting Gettysburg makes a good model of Roman combat) has an attritional combat model in which units degrade in combat over the course of about half an hour (all things being equal). This means that the side able to feed in reserves late in the fight will have a huge advantage, and that outflanking movements should have time to march, deploy and attack while front lines are engaged, but it is not certain - the front might give way first. Playing with the parameters of such a model and seeing how well they fit battle descriptions can be useful.

On the goals of this discussion - I think we have two (not mutually exclusive) camps of discontinuous combat:

- the 'dynamic standoff' model which is an account of low level interactions, which assumes a default state of close proximity but not contact (except missiles) interspersed with flurries of hand to hand combat which, if not decisive, revert back to the default state as the combatants back off.

- the 'battles are more complicated than you think' model, which is at a somewhat higher level and assumes that simple battle accounts obscure lots of detailed small unit interactions which take time and involve varying amounts of contact, resulting in combat that is discontinuous for small units while appearing continuous on the larger scale (of whole battlelines).  I think this is where I stand.

Against this, one continuous model:

- the 'multi hour hack' model - if a battle acount says the armies were engaged for hours, it means that all units were constantly engaged in one go all along the line all the time, solid block v. solid block, immobile.

Are those fair?

For a full account of the dynamic standoff and arguments for it, read Philip Sabin's 'The Face of Roman Battle' (Journal of Roman Studies 90 (2000) pp 1-17) and, in an earlier version, published in Slingshot - if you've got the 50 years DVD, you've got the earlier article. I can give a summary of the argument here if anyone would like it.

[Patrick Waterson]

I think continuity may be too much for a single step.

Maybe we should start by collecting and identifying evidence for duration first.
(It seems safer to interpolate continuity from duration, than it does to extrapolate continuity from a model of practical endurance.)

This was my first thought, too, but I had naively assumed that nobody would see fit to assume that duration of itself necessitated a discontinuity 'which is not described in the sources'.

Next I'd suggest that collecting evidence for casualties gives us casualties per unit of duration and some useful inferences concerning continuity.

Winners' casualties might have this effect, although I am not sure we can count on a direct relationship and there is bound to be someone who questions the figures.  It may be an interesting route to attempt, given the number of men on each side actually in contact with the enemy (as opposed to, say, elephants) and a comparison of battles between similar opponents.  One problem with classical casualty records is they tend as a rule to give only the dead; the few mentions of wounded show massive variability, from 50% of deaths (Caesar at Munda) to 10,000% of deaths (Josephus at Jotapata, with one hundred wounded for every death).  Without knowing the number of wounded, calculating how many blows were landed - or rather how many were effective against an opponent with a particular type and level of protection - will be a somewhat uncertain exercise.  (I once had peripheral involvement with a study on British armour losses in the Western Desert in WW2 - it was impeccably statistically based and totally and utterly misleading, as was amply demonstrated when an attempt was made to apply it to the Battle of Medenine.  Different techniques can make a huge difference to outcome.)

Lastly (I guess there might be some miracle quotes on endurance out there, but short of finding them...), rather than leap to analogies like boxing or riveting, wouldn't it make more sense to use out of period data. While musketry sources might not do much for us, there is probably some useful stuff on duration, casualties, endurance and continuity lying in the out of period cavalry and melee descriptions.

Perhaps, although even in 1815 few accounts are by watch-holders noting exact timings.  We can see that default infantry practice (as noted by Clausewitz in vom Krieg) is for two lines to halt and blaze away at each other with decreasing effect at short ranges until they run out of ammunition (at which point, particularly in the American Civil war, they sometimes start throwing stones) and this goes on indefinitely but once again without clear timing – apart from how long it would take to exhaust a unit's ammunition supply (which was often more than an individual's official allowance, cf. The French grenadier who told Napoleon "My hands have fired 120 cartridges this day").  So I get the feeling there will be the same old special pleading for alleged unmentioned discontinuity.

[Patrick Waterson]

Riveters took five years to train because the shipyards were riven with restrictive practice and you could only get the better jobs by awaiting your turn. The whole farrago fell apart when competitors entered the market with new techniques and no restrictive practices.

While sadly true of later years, this was not the case in the early 1900s when British shipyards were the best and most efficient in the world.

Richard Hough in The Big Battleship gives this description of riveting teams in action:

"As always, it was the riveters – the infantry of the working force – who were most in evidence and the creators of the most noise.  They were everywhere, hard up against the plating interminably riveting steel to steel.  Below them in little conspiratorial groups were the rivet-heaters, stirring their fires with bellows, turning to a glowing scarlet their lengths of steel, and then tossing them with invariable accuracy and speed up to the rivet-catchers above, who caught them in tins for rapid insertion and hammering.  It was a marvellous non-stop performance.  To anyone who paused on the yard and watched this process – or a dozen more of like skill – the deftness and rhythm had a spell-binding fascination."

This description of continuous moderate-tempo activity struck me as the kind of thing we should expect in a long-drawn-out classical infantry fight.  Roy rightly points out that rivets do not fight back, but the degree and duration of human effort involved, and the tempo, look about right to me for what we would expect from a sustained infantry fight between protected units.  This removes one of the principal props of the discontinuous combat theory, namely that the human frame is allegedly incapable of significant sustained effort.  The other main prop, lethality rates, has some rather more involved explanations which I shall enter into another time.

However, to Patrick's examples from Ammianus, the first does as Patrick  concedes sound susceptible to punctuated fighting, with repeated attacks.

This is because it is the Persian van trying its luck in a series of short assaults and skirmishes.  The point is that where discontinuous battle exists (essentially a skirmish between parts of the armies) Ammianus describes it as such.  Where it is not discontinuous he describes it as continuous, much to Richard's annoyance. ;-)

The second example is skewed because the Persians do not stand up to the Roman attack.

That is a classic, Roy: the example is skewed because one side wins. 

Seriously, and Richard also please take note, Ammianus is describing what the whole army is doing and doing together: it is drawn up in a noticeable formation (a crescent), it advances at an unusually rapid pace, the signal for battle is given – there is useful detail here, which Richard seems to have missed – and "the Roman infantry in close order with mighty effort drove the serried ranks of the enemy before them".

We then look for any indication that battle was discontinuous, that there were ebbs, flows, reliefs or renewed or repeated attacks.  There are none: "the clash of shields, the shouts of the men, and the doleful sound of the whirring arrows continued without intermission."  No amount of special pleading will get out of that, sorry.  To suggest that parts of the line took turns to generate noise and activity when we have been told the whole army advanced and engaged as one makes no sense.

Interestingly, though the Persians shoot as they retreat. Given that it would be exceedingly difficult to shoot at close range  at ranks of the enemy that were engaged with your own front ranks is it possible that the Persians are breaking off far enough back to engage in bowfire before the Romans come on again.

Yes, although not 'before the Romans come on again', but because this is the end of the battle; the Persians have had enough and are leaving the field Parthian-style: we note the very next thing to happen is that the Roman recall is sounded and the Romans retire back to their tents, battle over.

Of course there is the potential problem that the author's description is both linear and comprehensive so the battle is described as a unity whereas in reality there are different actions going on at the same time ...

This is in danger of becoming a topos: we cannot accept any account displaying continuity because there must have been discontinuities.  This, it seems to me, is not a viewpoint so much as an a priori obsession.  So, as nobody should have their beliefs go unheard, I ask: what originally brought about this way of looking at classical combat?

[Patrick Waterson]

On the goals of this discussion - I think we have two (not mutually exclusive) camps of discontinuous combat:

- the 'dynamic standoff' model which is an account of low level interactions, which assumes a default state of close proximity but not contact (except missiles) interspersed with flurries of hand to hand combat which, if not decisive, revert back to the default state as the combatants back off.

- the 'battles are more complicated than you think' model, which is at a somewhat higher level and assumes that simple battle accounts obscure lots of detailed small unit interactions which take time and involve varying amounts of contact, resulting in combat that is discontinuous for small units while appearing continuous on the larger scale (of whole battlelines).  I think this is where I stand.

Some actual evidence for this view would be nice.  Of course it may be hard to come by if the central thrust of the thesis is that this evidence is always omitted from battle descriptions ...

Let me give you a bit of help.  Try Dionysius of Halicarnassus VIII.65.2-3.

And then there is the problem that, as expressed in the classic maxim: "In war, only what is simple can work."  Patterns of subunits flowing in and out of contact are fine for skirmishing but will receive a bloody nose against a solid battleline.

Against this, one continuous model:

- the 'multi hour hack' model - if a battle acount says the armies were engaged for hours, it means that all units were constantly engaged in one go all along the line all the time, solid block v. solid block, immobile.

Are those fair?

Not really: if a battle account by an author with a military background* says armies were engaged for hours, it means the fighting lines were engaged for this length of time.  Some actions moved over the ground, some did not.  Some had ebbs and flows while remaining in contact; some had temporary collapses which broke contact and were rallied before resuming contact.  Some armies had reserves and/or reserve lines to commit; others did not (or relied on depth).  And some armies – particularly the Republican and Early Imperial Roman – were specifically configured for long-drawn-out affairs.

*Descriptions by men of letters tend to involve a lot of 'the fighting went on a long time with heavy losses to both sides' - while this is indicative of what was expected, it tends to appear in situations where the opposite is indicated, e.g. in Diodorus' account of Alexander's fight with Darius' bodyguards at Issus, so the reliability of such statements is uncertain, nice though it would be to be able to use them.

For a full account of the dynamic standoff and arguments for it, read Philip Sabin's 'The Face of Roman Battle' (Journal of Roman Studies 90 (2000) pp 1-17) and, in an earlier version, published in Slingshot - if you've got the 50 years DVD, you've got the earlier article. I can give a summary of the argument here if anyone would like it.

It might be an idea for those who have not read it or about it.  I would be more interested in any actual evidence in support of it.  I think that for any viewpoint, approach or theory to have any validity it does need some source evidence, even if indirect, and not be contrary to the prevailing trend of our sources.  So - please bring on the supporting evidence.

[Erpingham]

The problem with the duration model is it only takes us so far.  We have already done it for some medieval battles.  But the estimates are often for the battle as a whole, which tells us little about continuity or otherwise.  Overall, discontinuity is a better fit but how does that compare to Romans or Greeks or "barbarians"?

Likewise, we looked at combat statistics from hoplite battles but, leaving aside discussions of accuracy, they told us little about the nature of combat except winners lost relatively few men killed.  Unfortunately, this fact was interpreted by the different camps in different ways, because of the different combat models used.  In other words, didn't help much.

I think it will be difficult to move on without a clearer exposition of Patrick's "continuous combat" theory.  It seems, from hints within the debate it may be quite an extreme interpretation (e.g. once men entered combat, they continued to hack away until they were cut down or bled to death).  But other points, there seems to be an acknowledgement that just receiving missiles from horse archers might count as continuous combat.  As I said, it would be good to be clearer.

Addendum : Having read Patrick's two comments written as I was writing this, it is very clear that there is a massive difference in interpretation of the Persian battlepiece, depending what the initial theory of combat is.  This is an exercise in interpretation not observation.

[RichT]

This is an exercise in interpretation not observation.

Indeed - that is the whole problem (well it isn't a problem in itself, it is a problem if people fail to recognise the difference). So round and round we go, Patrick insisting we present 'evidence' for alternative models, while interpreting texts to suit his own theories without even recognising that is what he is doing. This is how all these discussions end up.

Patrick - I'm happy to summarise Sabin's argument, but not to look up every one of his references for you. Sabin's article is fully annotated with appropriate sources, several of which I've quoted in this thread (not coincidentally, that's where I got them from). Go ahead and read the article yourself.

[aligern]

Rope a dope technique.
This was Muhammad Ali's way of dealing with George Foreman. Ali sat back on the ropes protecting himself and letting Foreman tire himself out. Bear to n mind that Foreman is a superbly trained athlete and gets a rest in between each round. Eventually Foreman tires sufficiently for Ali to be able to deal him decisive blows. Note too that Ali gets Foreman angry at the beginning in an an attempt to get Foreman to be more aggressive and exoend more energy.
https://en.m.wikipedia.org/wiki/Rope-a-dope

To me this seems like a good analogy for Roman combat against less disciplined, less hardened and less trained barbarians. If the continuity school were broadly correct then Foreman should not have tired significantly. He has only fought a few rounds, takes interstitial rests, is not getting much back in the way of punches from Ali, yet he becomes tired enough to give the edge to the other fighter.
One big demerit of the 'continuity' case is that, given that we are talking about several thousand men in contact both sides could become so exhausted that there would be no decision.

[Patrick Waterson]

The problem with the duration model is it only takes us so far.  We have already done it for some medieval battles.  But the estimates are often for the battle as a whole, which tells us little about continuity or otherwise.  Overall, discontinuity is a better fit but how does that compare to Romans or Greeks or "barbarians"?

Quite.  We also note that the mediaeval 'discontinuity', where recorded, seems to suggest bouts of 30-60 minutes during which both sides were harming or in a position to harm each other as opposed to the 15-20 minute sessions favoured by the adherents of discontinuity.  One dissonant element about attempting to compare mediaeval practice with classical is that mediaeval armies were only rarely predominantly melee infantry; more often they were combined arms armies with significant mounted and missile components, so as m'lud Erpingham has previously mentioned, mediaeval 'combat', particularly where English armies are involved, will include a 'showering with missiles' element which is often an inseparable part of the casualty-trading and exhaustion-inducing process, whereas with classical armies this process is predominantly and often almost exclusively infantry melee.

I think it will be difficult to move on without a clearer exposition of Patrick's "continuous combat" theory.

Patrick does not have a 'continuous combat' theory.  He merely notes that discontinuous combat is not supported by our sources.  This of course does not leave much by way of alternative options, particularly the way our sources read.

  It seems, from hints within the debate it may be quite an extreme interpretation (e.g. once men entered combat, they continued to hack away until they were cut down or bled to death).  But other points, there seems to be an acknowledgement that just receiving missiles from horse archers might count as continuous combat.  As I said, it would be good to be clearer.

The point at issue is whether - not to mention how - troops would bounce out of action for a rest 2-3 times an hour without the opponent taking advantage of the process, and why such a process does not feature in our sources.

Addendum : Having read Patrick's two comments written as I was writing this, it is very clear that there is a massive difference in interpretation of the Persian battlepiece, depending what the initial theory of combat is.  This is an exercise in interpretation not observation.

Then please give us the benefit of observation: what do the accounts (one skirmish, one open battle) say to your good self?

[Patrick Waterson]

So round and round we go, Patrick insisting we present 'evidence' for alternative models, while interpreting texts to suit his own theories without even recognising that is what he is doing. This is how all these discussions end up.

My learned friend writes as if I am the only one injecting any element of interpretation.  And we still lack evidence (as opposed to arguments) for 'alternative models'.

Patrick - I'm happy to summarise Sabin's argument, but not to look up every one of his references for you. Sabin's article is fully annotated with appropriate sources, several of which I've quoted in this thread (not coincidentally, that's where I got them from). Go ahead and read the article yourself.

From this, I take it my learned friend has no supporting evidence to add either for the 'discontinuity' approach or his own preference for a small unit complexity approach (if I have that aright).  If conversely he has any, he should feel free to air it.

Phil Sabin does reiterate his discontinuity arguments in his book Lost Battles, and they are no more convincing there, at least to me.