*Turing’s Cathedral*

The author is George Dyson and the subtitle is The Origins of the Digital Universe.  It is a first-rate, splendid book, causing us to rethink the origins of computing systems, the connections between early computers and nuclear weapons systems, how to motivate geniuses, and also the career of John von Neumann.  Here is one excerpt, I may be giving you more:

In 1943, Bigelow left MIT, reassigned by Warren Weaver to the NDRC Applied Mathematics Panel’s Statistical Research Group.  Under the auspices of Columbia University, eighteen mathematicians and statisticians — including Jacob Wolfowitz, Harold Hotelling, George Stigler, Abraham Wald, and the future economist Milton Friedman — tackled a wide range of wartime problems, starting with the question of “whether it would be better to have eight 50 caliber machine guns on a fighter plane or four 20 millimeter guns.”

Here is one Francis Spufford article about the book.  Definitely recommended.

Comments

How much ground attack was the fighter plane expected to do considering air dominance in the European theatre and our inferior armor? Perhaps they should have started with "should the Sherman have a better cannon and armor, or keep it terrible."

The Sherman's terrible cannon and armor probably saved lives by reducing the aggression of American armored forces, forcing them to rely on our massive advantage in air and artillery. A common complaint about American troops from the Germans was that as soon as the fighting started the Americans just sat down and waited it out until air\artillery would batter them into submission; if American armored divisions had M26's insead of M4's they might not have been so reticient to engage.

Is there any evidence that forces equipped with M26s or with high velocity 76mm Shermans behaved more aggressively and cost more lives? Moreover, would a few aggressive sorties (or even cauldron enclosures) have saved more lives in the end by ending the Western war earlier?

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"A common complaint about American troops from the Germans ..."

I gotta love that. Troops complained because the enemy was pounding them. Hey, Sparky, think about that next time before you invade.

Ironically, isn’t there a rough parallel in western troops complaining about insurgent IED’s etc?
(Sorry, got mis-posted below the first time)

No.

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The problem was the doctrine, that tried to use tanks to fight infantry and to use tank destroyers to fight tanks, which turned out not to work in practice. Also, the tanks were designed to be easy to transport and to manufacture which helped win the war if not every tank battle.

Right. There's more to a tank than cannon and armor. The German Tiger II had the best cannon and armor on earth. But they broke down constantly, were prohibitively expensive, and couldn't cross most bridges because they were too heavy.

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Many, many military hardware decisions chose an apparently "inferior" weapon for what turned out to be really good reasons on a strategic scale.

My favourite such decision is the English longbow, that was replaced by the muzzle loading musket. Now the musket had a much lower rate of fire, a group of musketeers can put down much less fire than the same number of bowmen. But bowmen require 10 hours practice a week for years, with muskets you round up a bunch of peasants, give them an hours instruction, and you are set. So for the resources needed to field an army of bowmen, you can field an army of musketeers 10 times as large.

Added bonus, when the war is over, you take the muskets off the peasants and send them back to the fields. The bowmen have to keep practicing so you have fully armed peasants who can cause trouble.

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Wonder if four "50 caliber" and two "20 millimeter" might have been an option.....

They'd have had different ballistics, and that might have made aiming a problem.

America has consistently come down on the less popular side in this debate and gone with air-to-air cannon that fire greater numbers of lighter bullets. Though today the debate is centered around larger calibers.

Yes I agree it's a no brainer: "whether it would be better to have eight 50 caliber machine guns on a fighter plane or four 20 millimeter guns.” - Clearly 8 50 cal. is better than four 20 mm. Greater range, greater stopping power, and considering that ammunition is spent rather quickly in any event the extra tiny bullets from the 4 peashooters would hardly make a difference in a short period of time. Not that I'm an expert in ballistics, just have a science background and read a lot, though not as much as T. Cohen!

One of us is confused. It looks to me like 20 mm = approx. 80 cal.

50 cal = 12.7 mm

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Is there any approximate relationship between caliber and stopping power / range. How much better is an 80 cal versus a 50 cal? Linear? Quadratic? Etc.

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KE and momentum are proportional to the cube of linear dimension (assuming shell length also scales with caliber), holding all else (particularly muzzle velocity) constant. So naively, lethality should scale with the third power of caliber.

However, there are other things going on: larger shells might go right through and fail to deposit all energy in the target, there may be a threshold against armor below which damage is zero (and not just lesser) with smaller shells than larger, larger shells might be able to accommodate explosive warheads or sophisticated fuses, larger shells might have more predictable ballistics, and obviously hit probability goes down some (though maybe not linearly) with fewer shots taken.

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That's not correct. KE is (mv^2)/2 while momentum is mv. A small fast projectile has little momentum compared to a large slow projectile with the same amount of energy, so the former tends to deposit its energy readily as compared to the latter which tends to punch through the target.

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Sorry about that Finch, you are right. I didn't read your reply correctly.

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I believe the 20 mm shell was big enough to contain some high explosive ordinance, giving them significantly more stopping power than a .50 cal. round, which could not.

This is why late-war German fighters adopted bigger and bigger cannons (up to 30 mm), because their primary targets were huge 4 engine bombers and a lot of HE powder was necessary to bring those guys down.

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How about 8 .30's on each wing ? 18 .45's ? 20 .22's ?? I shudder to think how many Red Ryder BB guns they would have had to consider.

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I knew there was a book that I planned to read before "The Rent is Too Damn High".

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Milton Friedman has talked about that time of his life, he ran regressions and told the engineers what to do, and learned an important lesson...a lesson we should all pay attention to I think

Funny that it calls Friedman an economist but Stigler a math-statistician.

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Ironically, isn't there a rough parallel in western troops complaining about insurgent IED's etc?

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in case people want to read a few of the original reports: http://cna.org/sites/default/files/research/0204320000.pdf

You'll see its more math and stat observation and less speculating based on intuition.

As the excerpt shows, many of the top post-war economists worked during the war doing basically operations research. I'd read about Wald's study of damage to returning planes but had never seen the actual report until you provided that link.

I'd like to see more reprints or descriptions of the statistical and OR contributions of economists during WW II, and how useful they were. E.g. what were the recommendations of that Statistical Research Group on the machine guns vs cannon question? If they recommended cannon, their recommendations were clearly not heeded -- even during the Korean War the US Air Force persisted in using 50 cal machine guns, and found themselves outgunned by cannon-armed MiGs. Only after that war did the USAF finally switch to cannon -- and then made another mistake by deciding that air-to-air missiles made air cannon obsolete and unnecessary.

There's a moderately interesting book about the contributions of economists (Simon Kuznets is the most easily recognizable name) during WW II: _Keep from All Thoughtful Men: How US Economists Won World War II_ by Jim Lacey, but it's about the macro planning of the war effort and how much the US economy could produce, and is frustratingly incomplete. E.g. although the economists pretty clearly were doing better planning than most of the generals, the book doesn't tell us how accurate the plans' forecasts actually turned out to be.

One final example: in Errol Morris's documentary _The Fog of War_, William S. McNamara talks about his study during WW II of the strategic bombing of Germany. He was impressed with Curtis LeMay; whereas other bomber generals focused on how many planes aborted the mission, how many tons of bombs were dropped, how many had to be jettisoned, etc., LeMay zeroed in on what really mattered: how much damage was done to the target, and how many US bombers were destroyed or damaged. It was like the Moneyball approach to strategic bombing.

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Fwiw, the review at http://www.amazon.co.uk/review/R9EC3T2C6QNH1/ref=cm_cr_pr_viewpnt#R9EC3T2C6QNH1 - "Misleading account" - offers an alternative perspective on the book.

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I may have to read the book. I found the excerpt interesting because of some recent Wiki browsing that wandered into 20mm aircraft cannon. I believe the commitee decided a battery of four 20mm was clearly superior. A position reached by all our allied and enemy air forces.

We stayed with the 50 caliber guns because the Air Corps spent the war failing to develop an acceptable adaptation of an existing, successful Hispano Suiza gun. And turned down the British when they offered both their successful aircraft adaptation of the Hispano and sound advice on what we were doing wrong.

I'm rather fond of this book for the technical history of large caliber machine guns:

http://www.amazon.com/Rapid-Fire-Development-Machine-Guns-Ammunition/dp/1840374357/ref=sr_1_1?s=books&ie=UTF8&qid=1331224414&sr=1-1

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The Americans can always be relied upon to do the right thing--after they have tried everything else.
- Winston Churchill, from my memory

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For those particularly interested in von Neumann I recommend the biography by Norman Macrae: John von Neumann, New York: Pantheon Books, 1992, 405 pp. I read it some years ago and came away convinced that von Neumann was the Einstein of the 20th Century. He made an astonishing range of deep contributions: quantum mechanics, computing, weather modeling, game theory. His last, and not quite finished book, The Computer and the Brain, is still worth reading.

Wasn't Einstein the Einstein of the 20th century?

For the win!

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