Learn English – Upon their visit or on their visit

I think the difference is that we use "to" when "visit" is a verb:

I can't think of a single reason to visit them.

and "for" when "visit" is a noun:

And what was the reason for their visit?

Of course, when "visit" is a noun, you will need to add an article before it (Get ready for the visit), a determiner (I am not ready for that visit) or a possessive pronoun like in the example.

If you want to use it without a modifier, then you can do as J.R suggested and turn it into a gerund.

It is an archaic meaning of "inform" in the sense "to create an impression on something", like a fingerprint on moist clay.

This trope, a commonplace in philosophical writing, would ultimately go back, I think, to medieval scholasticism at the intersection of metaphysics and epistemology (and from there back to Aristotle); the "form" of something was its essence, that which made it to be what it was. Does the mind go out and alter that which it knows? Or does that which is known create impressions on the mind? Yadda yadda yadda.

They (the limits of our understanding) do not create an impression on reality. They do not change reality.