# the reciprocal of mass

#### Deinonychus

##### Senior Member
Economy of force is one of the nine Principles of War, based upon Carl von Clausewitz's approach to warfare. It is the principle of employing all available combat power in the most effective way possible, in an attempt to allocate a minimum of essential combat power to any secondary efforts. It is the judicious employment and distribution of forces towards the primary objective of any person's conflict. Economy of force is the reciprocal of mass.
Source: article “economy of force” on Wikipedia

Good day, everyone!

The definition of the noun “reciprocal” in the Wordreference dictionary is “something that is reciprocal to something else”, but I’m unable to fully understand it in this context.

What does the word “reciprocal” above mean specifically?
(The word “mass” above means “force concentration”)

• #### Uncle Jack

##### Senior Member
It is difficult to know how accurate the writer is being in their terminology. In precise mathematical terms, the reciprocal of something is one divided by that thing. The "something" can be almost anything. For example, the reciprocal of 4, is ¼ (a quarter), and the inverse is also true: The reciprocal of ¼ is 4.

You can use reciprocal with physical terms and measurements. For example, period (the length of time between repetitions) is the reciprocal of frequency (the number of repetitions per period of time). A light that flashes every 3 seconds has a period of 3 seconds and a frequency of 20 a minute. Both terms ("a period of 3 seconds" and "a frequency of 20 a minute") mean exactly the same thing.

However, in less technical uses, "reciprocal" is sometimes used to mean "opposite", and sometimes writers get confused. Reciprocity is a particular form of being opposite. Whether it fits or not in your example, I cannot say.

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#### Deinonychus

##### Senior Member
I got an idea now, thank you very much owlman5 and Uncle Jack!😄

##### Senior Member
In military terms, an objective can be won by throwing a large mass of forces against it, or by using the minimum required. The greater the economy of force, the smaller the mass required. Or rather, speaking after the event, the smaller the mass used succesfully, the more we are likely to say that "the general has used economy of force".

#### cidertree

##### Senior Member
The doctrine is to employ all available combat power.

"Economy of Force: Allocate minimum essential combat power to secondary efforts."
"Mass: Concentrate the effects of combat power at the decisive place and time."

-- US Army Field Manual 3-0, Operations, 2001

It's discussed at length in this article from The US Army War College Quarterly.

#### PaulQ

##### Senior Member
Economy of force is the reciprocal of mass. =
Economy of force varies in inverse proportion to the force concentration - as the force concentration increases, the economy of force decreases, and vice versa.

#### Deinonychus

##### Senior Member
Thanks a lot for all your help, Keith Bradford, cidertree and PaulQ!

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