Sixty men can dig a post-hole in one second

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Discussion Overview

The discussion revolves around the concept of "rates of work" as illustrated through various humorous examples and logical syllogisms. Participants explore the implications of scaling work rates, particularly in unrealistic scenarios, and share anecdotes related to this theme, including references to orchestras and cooking. The scope includes conceptual reasoning, mathematical reasoning, and humorous interpretations of logic.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning
  • Humorous

Main Points Raised

  • One participant quotes Ambrose Bierce's definition of logic, illustrating the syllogism related to work rates.
  • Another participant notes that while the problems often use unrealistic numbers, they do not find this surprising.
  • Several participants share their favorite variations of the work rate problems, including those involving orchestras and cooking times.
  • One participant suggests that larger orchestras might play at a slower tempo, questioning the assumption that more musicians always lead to faster completion.
  • Another participant references Amdahl's Law, implying that adding resources to a project does not necessarily speed it up.
  • Multiple participants mention Hofstadter's Law, which states that tasks often take longer than expected, even when accounting for this tendency.
  • One participant humorously discusses the implications of faulty premises in logical reasoning, using examples from popular culture.
  • Another participant reflects on the limits of models in understanding work rates, emphasizing the importance of recognizing when tasks can or cannot be parallelized.
  • Participants engage in light-hearted banter about changing light bulbs and the absurdity of certain logical conclusions.

Areas of Agreement / Disagreement

The discussion features multiple competing views and humorous interpretations, with no clear consensus on the validity of the various work rate scenarios presented. Participants express differing opinions on the implications of scaling work and the nature of logical reasoning.

Contextual Notes

Some assumptions regarding the scalability of work rates and the conditions under which tasks can be parallelized remain unresolved. The discussion also highlights the humorous and often absurd nature of applying logical reasoning to real-world scenarios.

Stephen Tashi
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Whenever, I see those elementary algebra word problems about "rates of work", I think of Ambrose Bierce's definition of Logc:

(Quoting it from https://www.uta.edu/philosophy/faculty/burgess-jackson/Ambrose Bierce (Logic).pdf )

Logic, n.
The art of thinking and reasoning in strict accordance with the liitations and incapacities of the
human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a
conclusion—thus:

Major Premise: Sixty men can do a piece of work sixty times as quickly as one man.

Minor Premise: One man can dig a post-hole in sixty seconds; therefore—

Conclusion: Sixty men can dig a post-hole in one second.

This may be called the syllogism arithmetical, in which, by combining logic and mathematics, we obtain a
double certainty and are twice blessed.

(Ambrose Bierce, The Devil's Dictionary)
 
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Usually, those problems use numbers that are not so unrealistic. Sure, you cannot scale it arbitrarily, but that should not be surprising.
 
My favorite version of this: "It takes a 40-piece orchestra six minutes to play a particular Strauss waltz. How long will it take a 60-piece orchestra to play the same waltz?"
 
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Lol at Mr V
 
Vanadium 50 said:
My favorite version of this: "It takes a 40-piece orchestra six minutes to play a particular Strauss waltz. How long will it take a 60-piece orchestra to play the same waltz?"

40*6/60=4 minutes. I'm so good at these problems, I breeze right through them. :)
 
Must have left the waltzers panting...
 
Vanadium 50 said:
My favorite version of this: "It takes a 40-piece orchestra six minutes to play a particular Strauss waltz. How long will it take a 60-piece orchestra to play the same waltz?"

I might be completely wrong here, but aren't larger orchestras usually employed for slower pieces, and thus the 60-piece orchestra might be conducted at a slower tempo? So there may be something to that.
 
Matterwave said:
40*6/60=4 minutes. I'm so good at these problems, I breeze right through them. :)
"Okay, there are 6000 notes left to play. You take the first 100, you take the second 100, ...
Go!"
 
  • #10
I'm fairly certain it was D H I read this from but I tend to use "9 women cannot make a baby in one month"
 
  • #11
mfb said:
"Okay, there are 6000 notes left to play. You take the first 100, you take the second 100, ...
Go!"
Interestingly enough, if you have enough people in the band, you can reach a singularity where the whole piece is played before the conductor even finishes conducting the first downbeat.
 
  • #12
Syllogism arithmetical, in my experience, is applied frequently by IT project managers. This is contrary to Brooks' law (from "The Mythical Man-Month") which states that adding resources to a late IT project will make it later!
 
  • #13
My favorite has always been Hofstadter's Law: It always takes longer than you expect, even when you take into account Hofstadter's Law.

(Hofstadter is a big fan of Godel and Escher)
 
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  • #14
DaveC426913 said:
My favorite has always been Hofstadter's Law: It always takes longer than you expect, even when you take into account Hofstadter's Law.
(Hofstadter is a big fan of Godel and Escher)

He must have done work with Murphy. As one of his laws states...
Nothing is as easy as it looks, everything takes longer than expected and if anything can go wrong, it will, at the worse possible moment
 
  • #15
I wonder how many guys were in this guy's kitchen?



Vinny Gambini: Eggs and grits. I like grits, too. How do you cook your grits? Do you like them regular, creamy or al dente?
Mr. Tipton: Just regular, I guess.
Vinny Gambini: Regular. Instant grits?
Mr. Tipton: No self-respectin' Southerner uses instant grits. I take pride in my grits.
Vinny Gambini: So, Mr. Tipton, how could it take you five minutes to cook your grits, when it takes the entire grit-eating world twenty minutes?
Mr. Tipton: [a bit panicky] I don't know. I'm a fast cook, I guess.
Vinny Gambini: I'm sorry, I was all the way over here. I couldn't hear you. Did you say you were a fast cook? That's it?
[Mr. Tipton nods in embarrassment]
Vinny Gambini: Are we to believe that boiling water soaks into a grit faster in your kitchen than on any place on the face of the earth?
Mr. Tipton: I don't know.
Vinny Gambini: Well, perhaps the laws of physics cease to exist on your stove. Were these magic grits? I mean, did you buy them from the same guy who sold Jack his beanstalk beans?
 
  • #16
It takes one man 20 minutes to make grits, so there must have been 20/5=4 men in Mr. Tipton's kitchen. NEXT!
 
  • #17
With 9 women, you can get 9x the usual expected baby production rate.
You can organize them so you get 9months to the first baby, then one a month for the next 8... or just have this huge burst of productivity after 9 months.
With the possibility for simultaneous delivery, the production rate can get arbitrarily high.

When the premize is faulty, the logical result is also faulty... though still logical.
I think we all know this.

Ive seen smart replies to rates of work problems phrased like: your dad and your uncle build chairs...
... the reply goes: takes forever cause dad and uncle never did get along... or something.
 
  • #18
One of Heinlein's characters deadpanned that more than a few newly-wed women were so eager for their first child that they manage to produce one in only three or four months.

A short essay on why the model fails might make an interesting follow-up question. Some tasks can be split up and parallelised, some can't, and some can to some extent. Understanding the limits of your model is at least as important as being able to manipulate the model in the first place. Teaching this along with models might even put to rest some of the "...science...gets such wholesale returns of conjecture out of such a trifling investment of fact" (as Twain put it) comments. (There is no "naive" smiley...)
 

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