“His thoughts were hemmed in. One can only draw curved lines on the terrestrial sphere which, as they extend, forever meet with themselves. At such intersections we always encounter what we have already seen.”

“We all draw different lines. Sometimes they intersect. Sometimes they don’t. We agree on forms of evil, but judge degrees of it, saying only the worst of humanity is truly bad. And everything along the grey lines is subject to opinion.”

“But then, even in the most significant details of our daily life, none of us can be said to constitute a material whole, which is the same for everyone, and need only be turned up like a page in an account-book or the record of a will; our social personality is a creation of the thoughts of other people. Even the simple act which we describe as “seeing someone we know” is to some extent an intellectual process. We pack the physical outline of the person we see with all the notions we have already formed about him, and in the total picture of him which we compose in our minds those notions have certainly the principal place. In the end they come to fill out so completely the curve of his cheeks, to follow so exactly the line of his nose, they blend so harmoniously in the sound of his voice as if it were no more than a transparent envelope, that each time we see the face or hear the voice it us these notions which we recognise and to which we listen.”

“What's the Future? It's a blank sheet of paper, and we draw lines on it, but sometimes our hand is held, and the lines we draw aren't the lines we wanted.”

“If we can widen the range of experiences beyond what we as individuals have encountered, if we can draw upon the experiences of others who've had to confront comparable situations in the past, then - although there are no guarantees - our chances of acting wisely should increase proportionately.”

“But if some mind very different from ours were to look upon some property of some curved line as we do on the evenness of a straight line, he would not recognize as such the evenness of a straight line; nor would he arrange the elements of his geometry according to that very different system, and would investigate quite other relationships as I have suggested in my notes. We fashion our geometry on the properties of a straight line because that seems to us to be the simplest of all. But really all lines that are continuous and of a uniform nature are just as simple as one another. Another kind of mind which might form an equally clear mental perception of some property of any one of these curves, as we do of the congruence of a straight line, might believe these curves to be the simplest of all, and from that property of these curves build up the elements of a very different geometry, referring all other curves to that one, just as we compare them to a straight line. Indeed, these minds, if they noticed and formed an extremely clear perception of some property of, say, the parabola, would not seek, as our geometers do, to rectify the parabola, they would endeavor, if one may coin the expression, to parabolify the straight line.”