# Translation, rotation, scalation?

I'm programming a math library and it never ocurred to me before now that most mathematicians say "translation, rotation, scale" to refer to these transformations. Problems arise when I want to distinguish the verbs "translate, rotate, scale" from the countable nouns "translation, rotation, scale". Is it wrong / strange to use "scalation" for the countable noun version?

• The typical escape is to use "scalings" as in Pseudopolar-based estimation of large translations, rotations, and scalings in images – Phil Sweet Jan 20 at 13:26
• @PhilSweet I'd agree except that I'd use the singular form in most cases. I have a feeling that the OP might be looking for a phrase like "the degree of scaling" to express the amount of enlargement or contraction of the shape under consideration. – BoldBen Jan 20 at 13:33
• Scalation means something else: thefreedictionary.com/scalation. Is there any danger of confusion between noun and verb in context? – michael.hor257k Jan 20 at 14:08
• There is nothing wrong with "the degree of scaling". – Peter Shor Jan 20 at 20:18
• @BoldBen Yes, that is the meaning of the word I am looking for. However, it is very verbose to use in a programming library. – Dexter André Jan 21 at 15:30

In English, if you want to turn a verb into a noun, and there's not a noun that already exists for it, we commonly use the gerund formed by adding -ing. And sometimes, even if there is a such a pre-existing noun, we use the gerund instead.

Thus, we say

I like swimming and hunting,

and not (unless we are trying to sound ridiculous)

? I like natation and venery.

So scaling is the most natural noun to use in parallel with translation and rotation.

• Thank you for your answer. I accepted this as my answer because it is general and will help me in the future if I encounter such a problem again. – Dexter André Jan 23 at 14:27

Scale is not a noun that means what you want. If you look at any dictionary, none of the definitions of "scale" refer to an instance of the transformation. The correct term is scaling. This is a Google search for scaling. It's sense 3 of the word, definition 2, and what you want is "scaling," gerund or present participle.

scale

represent in proportional dimensions; reduce or increase in size according to a common scale.

This is a verb, but never a noun that refers to the action of scaling.

• "Translation, rotation, scale" are often used - for example: w3.org/TR/SVG11/coords.html#TransformAttribute – michael.hor257k Jan 20 at 20:57
• @michael I only see "scale operation" used, which is fine, not "scale" by itself. – Matt Samuel Jan 20 at 21:06
• @michael For the other two it says "translation" and "rotation" alone. – Matt Samuel Jan 20 at 21:07
• Good point. And scale operation might be a better choice than scaling for OP too. – michael.hor257k Jan 20 at 21:31
• Thank you very much for your answer. I am afraid that the world of mathematics and graphics programming are butchering proper English, but it is very common in these fields to refer to scale as a noun. For example "I applied a scale to the object" would not sound wrong in such a conversation, even if it is not proper use of English. I will use "scaling" as the noun version of the word. – Dexter André Jan 23 at 14:24