Yes, further research shows that metanoia was a later development, although the 'turning around' or 'noetic conversion' is its exact meaning. Also similar to Plotinus 'epistrophe'.

@Wayfarer First off, I must apologize if I am, as I suspect, barking up the wrong tree but from what I gather, you seem to be interested in mathematical realism which I reckon falls under the rubric of Platonic Realism.

Mathematical realism, like realism in general, holds that mathematical entities exist independently of the human mind. — Wikipedia

You might wanna take a look at Synesthesia and grapheme color synesthesia

Some excerpts below for your consideration:

Grapheme–color synaesthesia or colored grapheme synesthesia is a form of synesthesia in which an individual's perception of numerals and letters is associated with the experience of colors — Wikipedia

Reports include feeling sensations in the hands or feet, coupled with visualizations of shapes or objects when analyzing mathematical equations, physical systems, or music. In another case, a person described seeing interactions between physical shapes causing sensations in the feet when solving a math problem. — Wikipedia

The point is, for (some) synesthetes, numbers have colors like an apple or a banana has and some math problems can give you the sensation of being physically touched! Are numbers real like apples, bananas and the hands of a masseur on your feet?

That tree is number 7 and smells fishy.

Hey only kidding. What impresses me about platonic realism is that numbers and fundamental concepts are not the product of your mind or mine, but can only be grasped by a mind. Whereas the tendency of empiricism is to attribute reality only to things that exist in space and time - the expression is ‘out there somewhere’. So they’re real in a way that sense objects are not.

That tree is number 7 and smells fishy.

Hey only kidding. What impresses me about platonic realism is that numbers and fundamental concepts are not the product of your mind or mine, but can only be grasped by a mind. Whereas the tendency of empiricism is to attribute reality only to things that exist in space and time - the expression is ‘out there somewhere’. So they’re real in a way that sense objects are not. — Wayfarer

:up: It looked like a good lead to follow and I thought you might be interested. Like they say somewhere in a little town in America, don't forget to be awesome! G'day.