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“But all of these concepts suffer from the same problem: For equality, inferiority, or superiority to have any meaning, what is being compared must first be commensurable. A symphony is not equal to an automobile. Nor is it inferior or superior. They are simply not commensurable.”
To invoke a more familiar example of incommensurableness: you can't compare apples and oranges.
The concept of "equality" (or the lack thereof, "inequality") is formally defined in mathematics. Whereas practically everyone knows that 2+2=4, many people might not realize that the claim, "Two apples plus two oranges equal four pears" is a meaningless statement. The reason such a statement, though numerically reasonable, is mathematically meaningless has to do with mixed units (or dimensionality). Thus, in order to make rational comparisons between objects, even related objects such as apples, oranges, and pears, one must first establish a common unit for comparison of those objects. In this instance, it could be, by agreement, units of fruit.
Dimensional analysis, by which one can establish whether or not a physical equation, involving quantities having various units of measure (such as energy, distance, time, etc.) can possibly make sense, is a very useful analytic tool. If both sides of the equation do not have (or can not be reduced to) identical combinations of units, then the equation can not possibly be meaningful.
Unfortunately, in the real world of sociopolitical discourse, such niceties as commensurableness are frequently ignored. But the consequences of such ignorance can, and often do, add up to dramatic waste of time, effort, and wealth, through bad blood, bad policy, and many tears of frustration.
Post 1,730 On Apples, Oranges, and Dimensional Analysis
My article "On Apples, Oranges, and Dimensional Analysis" was first published November 10, 2011 at 6:32 pm on the Technorati web site. I am reproducing it here today, in accordance with Technorati's cross-posting policy.
— TheBigHenry (AKA Henri LeGrand)