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A question which semi-regularly comes up here is "How [strong, fast, hungry, etc.] would [something] be if I scale its dimensions by [factor]?"

So we have some common language, let's call the scaling factor S in this question. Drawing from Gulliver's Travels, a Lilliputian (human, scaled down 10x) has S=0.1, and a typical resident of Brobdingnag (human, scaled up 10x) has S=10.

How can we easily distinguish between the following common cases when discussing this?

  • S^0: [Attribute] is proportional to original size.
  • S^1: [Attribute] is proportional to length. "How many rods laid end-to-end?"
  • S^2: [Attribute] is proportional to area. "How much food will my field produce?"
  • S^3: [Attribute] is proportional to volume. "How much will my creature eat?"
  • S^(2/3): [Attribute] is proportional to area/mass. "How many of its own kind can an X lift when scaled, using the same muscles?"
  • S^(3/2): [Attribute] is proportional to mass/area. "How much more efficient is using the same material to make a bigger gasbag for my airship?"

A good system will be fairly easily read by newcomers, and understood at a glance by anyone who is around regularly. A single-common-English-word description for each class which is easily distinguished would be ideal.


Tagged as science-based and hard-science for questions which require these explanations, and outdated-science for typical uses of this scaling. Not mentioning (say) inverse-square relationships because those tend not to be an entire system being size-changed, and typically are easier to communicate.

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  • $\begingroup$ The word proportional has exactly one meaning when speaking about quantities. A quantity $a$ is proportional to another quantity $b$, written $a \propto b$, if there is a factor $k$ so that $a = kb$. There is no need to disambiguate because there is nothing to disambiguate. What you probably mean is that such questions need to make it clear about what quantities they are asking. $\endgroup$
    – AlexP
    Dec 9, 2021 at 2:38
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    $\begingroup$ While a valid attempt to prevent misunderstandings, I'd dare say that simply asking people to edit their question to better explain their goals as a simpler alternative to solve this issue and much more friendly to newcomers, since it requires no new knowledge about any specific codes exclusive to this site. $\endgroup$ Dec 9, 2021 at 3:10
  • $\begingroup$ Yes, both would be nice. But I tend to see requests for clarification ignored, possibly because it's very easy to intuitively understand yourself and thereby miss alternative interpretations of your own words. (Case-in-point: I'd thought "easily read by newcomers" ruled out "specific codes exclusive to this site", but I now know better.) $\endgroup$
    – Anon
    Dec 9, 2021 at 6:03

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