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- The middle brow chain email, "Dibert's Salary Theorem," states that because the following conditions are true
- [Premise 1.1] Knowledge = Power
- [Premise 1.2] Time = Money
- [Premise 1.3] Power = Work/Time
- The following is true:
- Conclusion 1) Money = Work/Knowledge. Therefore, holding work constant, more knowledgable people are paid less.
- At first glance, it looks like this conlusion has been reached via algebraic errors or misinterpretations of folk idioms. But there is not a mistake in the algebra, nor does this chain email's author make any play off the english language. Indeed, a brief search finds that this text has been translated into other languages without a hitch. I like to think I am not mistaken in a belief that Knowledge is a type of Power, time gained equates to money gained, or that Power, of many kinds, allows you to perform work faster.
- There are several reasons this chain email is nonsense, but there is only one reason that it is nonsense which clearly opposes intuition.
- This mistake is subtle and crucial enough that it could actually have been made genuinely, by someone is a bitter state of mind. This is a mistake you likely made dozens of times in math and physics classes: the definition of the variable Money as used by Premise 2.3, and by Premise 2.2's version of the idiom "time is money," does not match the definition used in Conclusion 1.
- When "Time" appears in Premise 1.3, it describes Time _spent_ by a person. Premise 1.2 states taht time spent by a person equates to money spent by a person. But in the Conclusion, the variable "Money" is taken to mean money _gained_ by that person.
- To be clear -- you do not need to disbelieve Premises 1.1-3 in order to disbelieve the Conclusion.
- We can make this error easier to find by turning the problem into a quantitative story problem, one that removes the ambiguity of English and the emotions of doubt associated with Premises 1.1-3.
- There is a Goblin Kingdom where the Goblins do one of two things during the day, guiding Donkeys in pulling stones up a hill, or panning for gold.
- The King Goblin has instituted a rule: Every Goblin is entitled to a number of Donkeys equal to their score on the Goblin Record Examinations. In this way, a Goblin's knowledge is equal to its power, since for each Donkey under their watch, a goblin is able to pull one stone up a hill per day.
- Meanwhile, Goblins who pan for gold get one coin per day. In this way, a Goblin's time is its money.
- The Mathematician Gobin appears before his King and exclaims that there is a dire problem -- the Goblin Kingdom's economy must be failing in ways both practical and moral. The Mathematician Goblin uses this reasoning to conclude it:
- [Premise 2.1] (GRE Score) = (Number of Donkeys)
- [Premise 2.2] (Days spent NOT watching Donkeys) = (Number of gold coins collected)
- [Premise 2.3] (Number of Donkeys) = (Stones pulled up hill)/(Days spent watching Donkeys)
- From these premises it follows that
- (GRE Score) = (Stones pulled up hill)/(Days spent watching Donkeys)
- (GRE Score) = (Stones pulled up hill)/(Number of gold coins collected)
- [Conclusion 2] (Number of gold coins collected) = (Stones pulled up hill)/(GRE Score). Therefore, a Goblin's reward for moving a single stone up a hill is greater, if he has a lower GRE Score.
- Here the substitution of time spent for time gained is more apparent.
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