Reassessment of Italian Combat Prowess

[JonS]

It's simply an indisputable biological fact that every single German male that was of military age between 1939 and 1945 was alive before the war even began. Therefore the maximum size of the army was already set in stone before the war even starts.

Not really, because they kept expanding the pool of what was acceptable. They did it in Germany by upping the maximum age, dropping the minimum age, and letting in folk who would previously have been given a medical or occupational exemption. They also increased the pool by letting in outsiders - first the Austrians, then eventually anyone from ... well, considering they had an Indian contingent, and that guy from Korea, they were basically accepting anyone.

[JasonC]

ArgusEye wrote "some things are sufficiently WRONG that I cannot resist. It isn't aleph one curves. Quit that." So confident that the continuum hypothesis is false, are we? I know it is true, so there lol.

The curves in question are continuous, and the cardinality of all continuous functions on any finite interval is the same as the cardinality of the reals. It isn't less than the cardinality of the reals, because it contains the constant functions. And it isn't more than the cardinality of the reals, because each continuous function is defined by its values on all rational points (since it is continuous, and the rationals are dense), so there is a one to one mapping between sequences of rationals and these functions, and all (convergent) sequences of rationals is the definition of the reals. (I can define function distances in multiple ways to get the metric that establishes the correspondence, but any one suffices; the rational sequences will converge because they approximate a continuous function on a finite interval).

Leaving only the quibble, is the cardinality of the continuum equal to aleph one - which is the continuum hypothesis stated. Yes I am having fun with it, no there is no reason to "quit that", and no it isn't even remotely "WRONG" in block capitals.

But as with similar perfectly clear arguments to anyone who understands their terms, I never cease to be entertained by those who think their authoritarian pronouncements, personal opinions, red herrings and sophisms, matter a darn, or that the man in front of them requires their permission to reason, in utterly clear and simple ways.

[JasonC]

As for the imaginary quality, asked and answered. By late 1944, yes they were scraping the bottom of the barrel - though also transferring perfectly fit and even trained men from the other services. But the new formations of late 1943 and early 1944 hardly had to make do with poor material, as their subsequent field performance made clear. The allies thought many such quite new formations were hardened vets of the eastern front, at the time. They clearly could not tell the difference.

There is only one meaningful sense in which the German army of early 1944 might be said to be weaker than the early war German army, say especially of mid 1941. That would be leadership. The Germans sacked some of their best higher commanders by the fall of 1942, and while some of those who replaced them were competent, not all were, and the best minds were put out to pasture or relegated to lesser roles, and not trusted even with the full exercise of the commands they were given (e.g. Rundstadt in France).

This wasn't the result of attrition or being worn down by war, it was a purely self inflicted piece of folly, but it did meaningfully reduce the skill with which the war was directed. Hardly the strength of the army, however - more how it was directed to fight.

As for the nonsense about the army being stronger when it was half the size because there were more civilians who hadn't been drafted, you might as readily claim the army was better armed when there were fewer Panther tanks and more raw coal and iron ore lying around, instead. It is just nonsense - to translate potential into actual military power is not trivial, and the superior performance of the allies on that score actually decided the war. The Germans not trying very hard until they started losing is not a sign of their strength, but of their arrogant underestimation of their enemies and the basic incorrectness of their entire strategic conception of modern war, as something that could be fought quickly from small stocks rather than over long periods with large flows, and decided by something other than large scale attrition processes.

They were stronger late precisely because they gradually learned better on that score and actually exerted themselves, in both armaments production and manpower mobilization terms. Not enough, and above all not soon enough, to be sure.

[dieseltaylor]

I just got done reading a book "At All Cost" (good book) that I believe is the only story I have read that even mentions the Italian Air Force, and Navy. Very strange hearing about Italian subs. For some reason I didn't think they had any becuase I never heard anything about them.

From my current reading , the two last books of Nicholas Rankin,:

Churchill's Wizards: The British Genius for Deception 1914-1945. Faber and Faber. 2008. ISBN 978-0-571-22195-0.

Ian Fleming's Commandos: The Story of 30 Assault Unit in WWII. London, Faber and Faber, 2011. ISBN 978-0-571-25062-2

I am getting more insights into the non-ground force Italian story. I have also just inherited "Courage Alone: The Italian Air Force 1940-43" which will help get a feel for that area. Looks a very good book .

[JonS]

Its old quantity vs quality debate.

If this was directed at me, then the answer is no. It's neither quantity OR quality.

Take GOODWOOD as an example again. According to orthodox theory the British had preponderance coming out the whazoo, whether measured by raw numbers, force-to length ratio, or force to space ratio. They also had a marginal technology edge, or a significant technology edge if airpower is included. But none of that mattered because they failed to apply even rudimentary combined arms. The result we see is great gobs of tanks swanning around in the open ground east of Caen being shot up willy-nilly by German towed guns arrayed in great depth, to which the unsupported British tankers had no counter. The outcome was a contained offensive with high casualties. In a way it was analogous to the WWI attacks which failed due to a few unsuppressed MGs - all the preponderance and firepower in the world won't help you if in the end you're throwing unsupported massed infantry against MGs, or unsupported massed tanks against concealed towed guns.

In summary, the Germans at GOODWOOD had a deep, well concealed modern-system defense with ample reserves. The British tried to overcome that with an exposed, non-modern-system attack. They failed, and that failure had nothing to do with quality or quantity.

[76mm]

If this was directed at me, then the answer is no. It's neither quantity OR quality.

You've tried to describe Biddle's "insights" several times, and frankly I haven't seen anything which is not rather obvious, if not trite. Victory depends on how armed forces are employed--surely this is no surprise to anyone?

The quantity vs quality calculus is not necessarily based on the quantity and quality of the equipment, as you imply, but of the overall force, which includes leadership and tactics. In your Goodwood example, the German force was better than the larger British force.

Perhaps Biddle's writings contain some insights but so far I don't see them...

[JonS]

Perhaps it is rather obvious, even trite. Yet here we are, at post #206, with at least one person still vigorously trying to assert that the German army of 1944 was stronger than the 1940 edition simply because it was bigger and had shinier toys.

Preponderance and technology explanations of military power have extraordinarily deep roots. The benefits of them are primarily their simplicity - they're easy to explain, understand, and to visualise. They also seem to scale from personal experience. But they're about as accurate as flipping a coin.

I have little doubt that I've done Biddle's work a grave injustice with my oversimplified explanations of my limited understanding of his capability model. The full model has some 20-odd variables, and a 30-page appendix to explain it. What he is attempting to create is a predictive model that can look into the future, but as a byproduct he's also created an analytical model that can help explain the past.

You say "Victory depends on how armed forces are employed--surely this is no surprise to anyone?" The answer to that is, well, yes it is. Recent and ancient history is littered with pundits, commanders, and rulers who were surprised by exactly that.

Losers generally don't go into a battle, campaign, or war expecting to lose. But they do lose anyway. Blithely saying "the German force was better than the larger British force" doesn't really tell us anything useful. Better how, exactly? Because their army was smaller? Older? Not deployed in enough depth? Had insufficient mobile reserves? Poorly implemented or omitted modern-system offensive or defensive tactics? Moved at a higher velocity? What was it, exactly, that the Germans were 'better' at east of Caen in July 1944, and how can you prove that in a meaningful and useful way?

Edit: If you fancy doing some reading, the first four chapters of Biddle's book can be found here.

[Apocal]

Perhaps it is rather obvious, even trite. Yet here we are, at post #206, with at least one person still vigorously trying to assert that the German army of 1944 was stronger than the 1940 edition simply because it was bigger and had shinier toys.

:S

He isn't saying that.

ASL Vet - with much less fighting power in those panzers than a late war Panzer division. A third with MG main armament, another quarter or so with 20mm main armament, etc. No, the early war PD was not a stronger force than a late war PD - the late war PD was, hands down. The latter had a tactically superior mix of weapons, tuned by experience; a better suite of all forms of support weapons; superior weapons in every role; superior coordination of all of the above, etc.

If given the same physical assets available in 1940, you reorganized the limited high impact ones along mid to late war lines, you could get more not less combat effectiveness out of them, in 1940. The actual tuning of the mix of assets improved over the course of the war. The changes made to TOEs and to typical tasking and such, were not debilitating consequences of mythical shortages or declining command ability, they were intelligent adaptations to lessons in the field.

At any rate, giving the same army more numbers and shinier toys will virtually ensure they are stronger. Of course, some people eat paint-chips and perform worse, but there always exceptions and that is pointing towards a better tool being poorly used, rather than anything wrong with the tool itself.

[76mm]

You say "Victory depends on how armed forces are employed--surely this is no surprise to anyone?" The answer to that is, well, yes it is. Recent and ancient history is littered with pundits, commanders, and rulers who were surprised by exactly that.

Losers generally don't go into a battle, campaign, or war expecting to lose. But they do lose anyway. Blithely saying "the German force was better than the larger British force" doesn't really tell us anything useful. Better how, exactly?

Jon, thanks for the link, the book is available for Kindle, so I've put it on my (rather long) wish list. I'm sure I'll read it sooner or later...

Regarding the text quoted above: actually, I don't think any of the pundits, commanders, and rulers were necessarily surprised by the fact that victory depends on how forces were employed--rather they have been surprised by the fact that their enemy was able to employ their troops better than they themselves could.

But from your explanation I now understand that Biddle is not just pointing out this fact as true, but is actually trying to quantify the various factors which make it true, which is obviously a much more challenging and potentially interesting undertaking.

[Sublime]

Eh.. I think you forgot to add Russian soldiers. I've read plenty of accounts where they just label every German tank a Tiger or something along those lines. I think that was less to do with German activities. More to do with terror knowing that if a Tiger appeared you were screwed, and perhaps good performances on the part of the Panzer Truppen who made it seem like they had better equipment than they did most of the time.

[ArgusEye]

ArgusEye wrote "some things are sufficiently WRONG that I cannot resist. It isn't aleph one curves. Quit that." So confident that the continuum hypothesis is false, are we? I know it is true, so there lol.

No; the continuum hypothesis is quite well supported. It is your assertion that is wrong.

The curves in question are continuous, and the cardinality of all continuous functions on any finite interval is the same as the cardinality of the reals. It isn't less than the cardinality of the reals, because it contains the constant functions. And it isn't more than the cardinality of the reals, because each continuous function is defined by its values on all rational points (since it is continuous, and the rationals are dense), so there is a one to one mapping between sequences of rationals and these functions, and all (convergent) sequences of rationals is the definition of the reals.

Go rationalize pi or Eulers number, then come back. Both real numbers.

(I can define function distances in multiple ways to get the metric that establishes the correspondence, but any one suffices; the rational sequences will converge because they approximate a continuous function on a finite interval).

You start with an error. The first thing you learn in higher mathematics: never lose track of what you are computing. You went wrong there. Even if we discard the obvious granularity of a computer graph [enough to invalidate your statement, but not 'mathy' enough] there is the question of someone making a graph. He is going to have less than real infinity enumerating the functions and/or datapoints. He has to define them. This alone means that he has a choice of at most countably infinite curves, limiting him to Aleph null. You cannot just raise the cardinality of his available input domain by assuming the entire output set is available to him. Trivial error. The rest is a clunky bunch of half-understood math jargon, instead of stating that you can map all points bijectively to a line, which would have sufficed for the continuum applicability.

Leaving only the quibble, is the cardinality of the continuum equal to aleph one - which is the continuum hypothesis stated. Yes I am having fun with it, no there is no reason to "quit that", and no it isn't even remotely "WRONG" in block capitals.

The continuum hypothesis is correct. But you are WRONG.

But as with similar perfectly clear arguments to anyone who understands their terms, I never cease to be entertained by those who think their authoritarian pronouncements, personal opinions, red herrings and sophisms, matter a darn, or that the man in front of them requires their permission to reason, in utterly clear and simple ways.

So spoke the walking sophism.

Whenever I read your posts, I see unfounded optimism about your analytical skills. You talk the math talk, but you can't walk the walk. If you can't even get simple applicability issues for cardinality [or in other threads, statistics] right, I cannot but shake my head. Your use of jargon, straw men, snow jobs, and half-assed bandying around of almost-correct-but-not-quite-understood mathematical terminology might impress the uninformed, but not me, buddy. You just look sad to me.

[76mm]

Eh.. I think you forgot to add Russian soldiers. I've read plenty of accounts where they just label every German tank a Tiger or something along those lines. I think that was less to do with German activities. More to do with terror knowing that if a Tiger appeared you were screwed, and perhaps good performances on the part of the Panzer Truppen who made it seem like they had better equipment than they did most of the time.

Sure, probably Russians too, although I have not seen as many accounts to that effect.

The point is that this kind of mistake is pretty common in war and not necessarily based on the efficiency of British riflemen.

[76mm]

ooh boy, math fight!

[JasonC]

Argus - more absurd attempts to make simple reasoning an activity requiring the permission of others, and once again it fails hopelessly. Sequences of rationals are not single rationals; all reals can be represented by such sequences; it is the bog standard way of defining the animals in the first place. That handles the absurd red herring reference to non rational reals, which just ignored the word "sequence" in the phrase it quotes.

Next to my alleged error, leaving aside the absurd red herring of computer anything, which no one else had ever mentioned, "what we are computing" is a comment on 76mm's prior post (containing the prescient observation that the thread was becoming absurd), "you could draw an infinite number of such curves, each of them different to some extent, based on what you are trying to graph and what you are trying to reflect." So no, we are not trying to use a computer to splice a line through n known datapoints, there is no prior countable set being mapped to the real domain; the exact thing we are calculating is the cardinality of all continuous functions on a closed interval.

And the number of those is the cardinality of the continuum - it is a bog standard result and one Argus undoubtedly knows. He prefers trivial geometric ways of proving it (that to me aren't revealing or proof like enough, even if elegant to one who already sees why).

No, "he" is not going to have less than infinite generating functions, and doesn't need to define them - the precise question spoke of graphs of different things, not any one thing, etc. 76mm or a hypothetical "he" is under no such constraint. Everything is contained in a simple "could" - any imaginable continuous squiggle might track something or other that one of 76mm's imaginary discussion participants might have wanted to graph.

That indeed had been 76mm's point and I was merely agreeing with him about it, with modest added "color", before pointing out certain characteristics that all such curves would still have, merely as continuous. And the whole point of that agreement and comment was to show how little of what others were railing against was even about the actual history, since much of it is merely formal and trivial.

Leave it to CMers to rail against the formal and trivial part - and the man in front of them - instead of just agreeing to the simple actual history point.

[sburke]

ooh boy, math fight!

Yeah really, I'm thinking to cut class and go get stoned. Up for a beer?

[Sublime]

Sure, probably Russians too, although I have not seen as many accounts to that effect.

The point is that this kind of mistake is pretty common in war and not necessarily based on the efficiency of British riflemen.

Yeah you've got a point. The Russian accounts tend to generalize more with slang with terms for German machine guns and whatnot. Almost like Allied accounts mentioning 'Spandaus' or 'Schmeissers'.

However I think at Mons the situation was first that the German troops made a misjudgement, but more so the pre-war British Army, with its incredibly high standards of training, especially in regards to fast, accurate rifle fire. Of course after Mons and the next few months the pre-war army was still killed off completely, more or less.

[ArgusEye]

Argus - more absurd attempts to make simple reasoning an activity requiring the permission of others, and once again it fails hopelessly.

Permission? Where did you get that straw man?

Sequences of rationals are not single rationals; all reals can be represented by such sequences; it is the bog standard way of defining the animals in the first place.

No. They are usually defined by series, I will assume you mean that.

That handles the absurd red herring reference to non rational reals, which just ignored the word "sequence" in the phrase it quotes.

You came up with the rationals comprising the reals. Not me. The cardinality of Z reaches only Aleph null. You limit yourself [needlessly] into error.

Next to my alleged error, leaving aside the absurd red herring of computer anything, which no one else had ever mentioned, "what we are computing" is a comment on 76mm's prior post (containing the prescient observation that the thread was becoming absurd), "you could draw an infinite number of such curves, each of them different to some extent, based on what you are trying to graph and what you are trying to reflect." So no, we are not trying to use a computer to splice a line through n known datapoints, there is no prior countable set being mapped to the real domain; the exact thing we are calculating is the cardinality of all continuous functions on a closed interval.

Bull. I refer to my earlier post.

And the number of those is the cardinality of the continuum - it is a bog standard result and one Argus undoubtedly knows. He prefers trivial geometric ways of proving it (that to me aren't revealing or proof like enough, even if elegant to one who already sees why).

A proof that is not proof like enough? What I wrote is no proof. What you wrote was confused gibberish.

No, "he" is not going to have less than infinite generating functions, and doesn't need to define them - the precise question spoke of graphs of different things, not any one thing, etc. 76mm or a hypothetical "he" is under no such constraint.

Reality tends to be a bitch. If you're going to try to show off by using obscure mathematical expressions, you need to get them right. Cantor came up with his cardinality structure exactly because of the kind of errors you're making. And now you're using his jargon to make exactly those errors. It would be funny if it wasn't annoying.

Everything is contained in a simple "could" - any imaginable continuous squiggle might track something or other that one of 76mm's imaginary discussion participants might have wanted to graph.

That indeed had been 76mm's point and I was merely agreeing with him about it, with modest added "color",

which you got wrong. Simple. Now you could bite your tongue and learn, and not be the same kind of wrong again, or you can rant and rail trying to put a shine on your failure, and set yourself up for the same failure again. I think I know which one you're going to come up with, but feel free to surprise me.

[Childress]

The cardinality of Z reaches only Aleph null. You limit yourself [needlessly] into error

C'mon, ArgusEye. That's easy for you to say.

[ArgusEye]

C'mon, ArgusEye. That's easy for you to say.

Allright, fair point!

I think I couldn't put it clearer than this gentleman:

Which contains the original Cantor proposals, although it lacks rigour in this formulation. For a rigourous treatment, any book on Cantorian mathematics will cover it.

[c3k]

This thread contains SO much sig material, I'm not sure where to start. I'll see your aleph 1 and raise you to aleph 2.

[Michael Emrys]

If you even had an aleph it would run away from home.

Michael

[76mm]

Whew, I'm willing to read a couple of posts on obscure math topics, but I draw the line at watching youtube videos about them. Next we'll be singing math songs or complaining about the lack of fibonacci curves on the alephant included in CMFI... I beg you, no more!

[Wodin]

WOW..this has to be the best ever flame war I've come across on the net..is it odd I'm finding it enthralling compared to the usual flame wars that go on?

I will say I never knew it was so complicated..Italian prowess that is..

[Erwin]

I didn't understand much of this.

Could someone please provide a crayon version interpretation? Many thanks.

Permission? Where did you get that straw man?No. They are usually defined by series, I will assume you mean that.You came up with the rationals comprising the reals. Not me. The cardinality of Z reaches only Aleph null. You limit yourself [needlessly] into error.Bull. I refer to my earlier post.A proof that is not proof like enough? What I wrote is no proof. What you wrote was confused gibberish.Reality tends to be a bitch. If you're going to try to show off by using obscure mathematical expressions, you need to get them right. Cantor came up with his cardinality structure exactly because of the kind of errors you're making. And now you're using his jargon to make exactly those errors. It would be funny if it wasn't annoying.which you got wrong. Simple. Now you could bite your tongue and learn, and not be the same kind of wrong again, or you can rant and rail trying to put a shine on your failure, and set yourself up for the same failure again. I think I know which one you're going to come up with, but feel free to surprise me.

[Sequoia]

Wasn't Aelph the Alien puppet who ate cats?