Monday, December 11, 2006

i was taught wrong proportions

Back in primary school(i guess that would be grade school for some people), i was taught that if 1 man completes a piece of work in 10 days, 10 men would complete the same piece of work in 1 day. i have since come to question the validity of that premise, because if we consider the men actually completing the work in 1 day:
  • as Prof Olicks mentioned, we're assuming that they all work at the same time, and they don't have to queue up the work - in other words, no person's work is dependent on any other person's
  • we're assuming there are no slackers among them, which is most likely not true. come on, any group of 10 people will almost certainly have one or more slackers.
  • we're assuming each of the 10 men has exactly the same rate of work as the 1 man - which is of course, not plausible.
  • we're assuming the men don't do anything to affect their work rate, either positively (like cheering each other on or smoking weed) or negatively (like...i dunno!).
  • we're assuming they even begin to cooperate.
  • we're assuming they don't get into each other's way, which will obviously slow down the rate of work.
  • we're assuming they don't go off, form a union and call a strike for some reason.
  • we're assuming having 10 men on the site isn't a violation of safety laws.
  • as Prof Biyi reminded me before i publish this, it also depends on the nature of the work. if it takes 1 man 1 minute to put on a pair of trousers, how long will it take 10 men to put on the same pair of trousers? i think that bears thinking about.
  • from Prof Biyi's postulation, we can also assume that we have not asked the employer of labour if he would be willing to pay 10 men as against 1, since the 1 has the (decided) advantage of not being able to form a union (of course, that doesn't stop him from getting a shotgun...).
  • since we learnt this before we found out about the law of diminishing returns, we can safely assume that we are assuming without the said law, which IMHO, has a bad habit of not knowing how to be ignored gracefully.
  • we're assuming that some other thing i haven't taken into consideration does (not) happen.
in my opinion, the smart answer to the question: "if 1 man takes 10 days to complete a piece of work, how long will it take 10 men to complete the same piece of work?" would be: "it depends".

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