Yep, I definitely do something similar. I respect Bret Victor greatly (his Magic Ink essay has had more of an effect on what I do as a career than almost any ot

Yep, I definitely do something similar. I respect Bret Victor greatly (his Magic Ink essay has had more of an effect on what I do as a career than almost any other single thing), but I've never really been completely on board with this idea -- though in fairness it's a response to an implementation of a very specific programming environment, it's not a general solution. Re mentally visualising, I'm reading a book called Mathematician's Delight[1] at the minute, and its first chapter has one of the neatest pieces of writing on abstract reasoning that I think I've ever read, it's reified a lot of instinctual ideas I had about how I program. I've clipped quite a lot of notes from it -- this in particular is relevant I think: "Beginners in geometry are sometimes puzzled by being told that straight lines have no thickness. We shall never, we are told, meet a straight line in real life, because every real object has a certain thickness. One of Euclid's lines, however, has no thickness. Two lines meet in a point, and a point has no size at all, only position. We shall never meet a point in real life, either, for all real objects have a certain size, as well as a certain position It is not surprising that pupils wonder how we know anything about objects which no one has ever seen or ever can see. This difficulty is a good example of the confusion which can come from misunderstanding the methods of abstract thought. We have seen that Euclid's geometry grew out of the methods used for building, surveying and other work in ancient Egypt, This work was done with actual ropes or strings, real linen threads with actual thickness. What does Euclid mean when he says that a line has no thickness, although he is using results suggested by the use of thick ropes? He means that in laying out a football field or in building a house you are not interested in the size or the shape of the knots made where one rope is joined to another. If you allowed for the fact that ropes possess a definite thickness, if you carefully described all the knots used by a bricklayer, you would make the subject extremely complicated, and no advantage would be gained. Euclid therefore says, if an actual rope has thickness, neglect this in order to keep the subject reasonably simple. The position is not that Euclid's straight lines represent a perfect ideal which ropes and strings strive in vain to copy. It is the other way round. Euclid's straight lines simplified account of the complicated way in which actual ropes present a rough, behave." [1] https://archive.org/details/mathematicians-delight-w.-w.-sawyer https://archive.org/details/mathematicians-delight-w.-w.-saw...