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Say we have two sentences that use understanding as a gerund:

Understanding how to open this door is crucial in the event of an emergency.

My understanding of physics is woefully inadequate.

What is the distinction between these two that calls for the inclusion of of in the second sentence but not in the first?

(I have an inkling that it's got something to do with the determiner, but I can't quite pin it down.)

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In the first sentence, understanding is a verb, used in its most common sense.

In the second one it's a mass noun. (OED) In this sense of the noun understanding, of would be required. Just like it would be in my grasp/comprehension/love/hate of physics...

For future reference, in cases where replacing understanding with to understand doesn't make any sense at all, it's a noun.

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    You might want to say that it's not an ordinary verb but a gerund, and hence can often be substituted by the to-infinitive.
    – user21820
    Apr 30 '15 at 16:31

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