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I have a problem with these two formulations:

A variety of self-sustained motion mechanisms in nature can be classified into just two groups: motion based on propulsion or on ratchet principles.

or

A variety of self-sustained motion in nature rely on two mechanisms: movement based on propulsion, or on ratchet effects.

In both cases there are a lot of nouns that just duplicate others:

  • motion mechanisms, motion principles
  • motion, movement
  • mechanisms, effects

Is there a way to say the same more concise?

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    [All] self-sustained motion in nature relies on [either] propulsion or ratchet effects. Include the "optional" words if you want the "gravitas" of a "universal law". But surely Newton got there first, and the Moon orbiting the Earth is "natural motion", but I don't see any propulsion or ratcheting there. – FumbleFingers Aug 26 '15 at 12:45
  • @FumbleFingers Nice comment, but I would humbly argue that the Moon orbiting the Earth is not self-sustaining its motion. – yarchik Aug 26 '15 at 12:49
  • Well, nothing lasts forever. I knew the Moon was (very slowly) receding from the Earth, but I've only just discovered that apparently it won't eventually "escape" and go haring off into space. How about the tidal motion on Earth (or does that not count either, since it's mainly caused by the Moon?). – FumbleFingers Aug 26 '15 at 13:36
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    It isn't always a good idea to be too concise. For instance, in the original sentence, motion is deleted before on ratchet effects by conjunction reduction. That's OK, but since you're making a point about what motion is, repeating the word motion is a good thing because it gives your audience (who may not be paying attention, after all) another chance to figure out what you're on about. – John Lawler Aug 26 '15 at 14:35
  • John has said it all. – Fattie Aug 26 '15 at 14:45
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Let's start with the original sentence.

A variety of self-sustained motion mechanisms in nature can be classified into just two groups: motion based on propulsion or on ratchet principles.

The first "duplicate" that you point out is "motion mechanisms". Let's move the words around a bit, though.

A variety of mechanisms for self-sustained motion in nature can be classified into just two groups: motion based on propulsion or on ratchet principles.

Mechanism isn't duplicating "motion"; it was part of a compound noun that I split up for illustration.

While it is encouraged to use different synonyms to avoid using the same word multiple times in the same sentence, a technical subject like this has a harsher treatment of synonyms. (Anybody else remember the "Canary Trap" from Tom Clancy's books?) While "motion" and "movement" are synonyms to the layperson, they are not in physics.

The only remaining qualm remains with the list following the colon. I would probably rewrite it as follows.

A variety of self-sustained motion mechanisms in nature can be classified into just two groups: motion based on propulsion and motion based on ratchet principles.

The original sentence was attempting to be too compact and resulted in a sentence that nearly needs two passes before you understand it. Technical writing is slow reading to begin with; we should aim to make it readable the first time through.

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A few more ideas for you to play with:

Self-sustained motion in nature may be classified according to two possible physical mechanisms: propulsion and ratchet effects.

OR

Self-sustained movement in nature has been found to rely on either a propulsion mechanism or a ratchet effect.

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