What is the nuanced difference between "at seeing" and "when seeing"?

Solution 1:

But one day a lonely pilgrim, whose heart burned with the pure flame of faith, so deeply grieved at seeing the desecration and decay of this place.

OP asks pertinently: What is the nuanced difference between “at seeing” and “when seeing”?

There might indeed be a fine difference of nuance between 'at seeing' and 'when seeing', but it would be illogical to explain it on the basis of the specific example given in this question, where 'when seeing' cannot replace 'at seeing' without sounding awkward, because in this particular sentence, as rightly pointed out by User26328 in the earlier, excellent answer (and I quote the relevant part here)

"(...) 'at' is not linked to 'seeing'; rather, it's linked to the prepositional valency of grieved: to be grieved at something."

Therefore, in order to address the question of the 'nuanced difference' between 'at seeing' and 'when seeing', we need to find or construct a good example sentence, which is one where we could grammatically replace 'at seeing' with 'when seeing' and the fine meaning changes as a consequence.

1.Such examples are uncommon because 'at seeing' and 'when seeing' are not usually used interchangeably. When I did a Google search with "when seeing" I found it used predominantly at the beginning of a sentence, most often in headings of news / lifestyle articles, and (quite unlike 'at seeing') very rarely used in the middle of a sentence.

Google search results for "when seeing"

Google search results for "at seeing"

2.Many common sentences present too simple an example, such as 'don't run when seeing a dog' / 'don't run at seeing a dog.' The obvious difference in meaning here would be, 'don't run when you see a dog' vs 'don't run at the sight of the dog': however there is no nuance in the difference.

So I have constructed the following pair of examples (which are closely related to the sense and gravity of the original sentence) in order to answer OP's question about 'nuanced difference':

We feel sad when seeing the decline of a great sportsperson.

We feel sad at seeing the decline of a great sportsperson.

[Pl. note that these would be more commonly written as 'we feel sad when we see the decline of a great sportsperson' and 'we feel sad at the decline of a great sportsperson' respectively.]

The straightforward semantic difference, as already pointed out by members in the earliest comments, would be that 'when seeing' means at the moment of / time of/ on the occasion of seeing while 'at seeing' means because of / effect on the viewer of seeing, but this does introduce nuance worthy of discussion.

What is the nuanced difference here? This is my own interpretation:

If we feel sad 'when seeing' (at the time of seeing) the decline of a great sportsperson, as for instance when a great player misses an easy penalty kick, it could be argued that maybe that feeling is specific to the moment / occasion of seeing, and does not persist after the event?

They felt a strong but fleeting sense of sadness when seeing the decline of the great footballer: missing that penalty kick was an awful reminder that he had lost his cutting edge, and was on the long, slow road to sporting oblivion.

Whereas 'at seeing' implies that the feeling is caused by what is seen (here, the decline of the great sportsperson):

He felt sad at seeing the decline of the great footballer: he was reminded of it often in the next few months -- years later he would come upon some reference and relive that sadness, thinking of how that missed penalty had heralded a giant's long, slow descent into sporting oblivion.

We feel that emotion because of it, not just 'when we see it' -- meaning that we could feel the same even on other occasions when we think of it -- that's the nuanced difference!

Solution 2:

On + present participles is a fixed grammatical construction that means when one + verb in the past tense.

On the other hand, at + present participles is not a fixed grammatical construction, so it doesn't mean anything on its own.

In at seeing, at is not linked to seeing; rather, it is linked to the prepositional valency of grieved: to be grieved at something.

If you had had another word (adjective or past participle used as an adjective), you would have had another preposition altogether: upset with seeing, bent on seeing, mad at seeing, typical of seeing, etc.

Solution 3:

at seeing - refers to a moment in time defined by 'seeing sth', as a noun in locative case; through the suitable preposition in context ('at').

when seeing - refers to an ongoing action 'seeing him' , as a verb in continuous progressive aspect : with the entire sub clause made to act as an adverb through the use of conjunction 'when'.