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Dagny excerpt-
…but the straight line is the badge of man, the straight line of a geometrical abstraction that makes roads, rails, and bridges, the straight line that cuts the curving aimlessness of nature by a purposeful motion from a start to an end.

Billthedrill...
And yet the straight line is not really an artifact of man, but his imitation of the horizon. The horizon isn’t perfectly straight, of course, either in terms of curvature or of granularity, but then neither are the lines made by men. In this man is one with his world whether he likes it or not.

and...
The truly straight line is, as Dagny just said, an abstraction, an artifact not even of man’s mind if Immanuel Kant is to be believed, but an a priori concept that is one of the laws of the universe that form the foundation of Ayn Rand’s epistemology.

You've made me consider the significance of this concept and I am not sure I understand the implications. Is not a plumb line straight? Used from the very beginning of mans efforts to build, it describes a perfectly straight line and man has always striven to copy its perfection.
The pull of gravity is a summation of all the the relevant forces but it resolves into a natural axis that is able to be harnessed by mans mind. In fact all other axis are derived from it.

I read the chapter and attributed Dagny's take on this as a flaw in her reasoning, but as you pointed out a straight lines non-natural existence is part of the basis of Rands epistemology. Had Dagny stood on the tracks holding a plumb bob in front of her, would she have seen the natural source of the straightness of the rails?

Perhaps it's one of those times when I'm looking for something that isn't there but so far the logic used by Rand appears valid to me.

Good stuff - Still Thinking caught my intention. You'll discover upon examining that plumb bob that the string is, even without a lens, coarse, its boundaries pocked and porous, its internal fibers twisted and lumpy. Nothing about the thing is straight upon close examination. It is only straight when you back up enough to consider it as a one-dimensional object, which it is only in the mind. Real things can approach straightness but pure straightness is an abstraction.

Philosophically this stuff is like dog-paddling in a mile-deep ocean. Enter Immanuel Kant. This idea of straightness, defined as a one-dimensional line describing the shortest distance between two points (themselves abstractions) - is it an invention of man, or was it always there and man merely its discoverer? A posteriori or a priori? Inventor or discoverer? (Bishop Berkeley versus John Locke in one famous example. I got a tenner on Locke by a TKO in six rounds...) It makes a fundamental difference in one's view of the universe.

The reason that Rand is so closely aligned with Aristotle on the topic but parts company when it comes to teleology is that for her the laws of the universe simply are, and for him they are caused. His is, in essence, one form of the teleological argument for the existence of God.

As I said, this stuff gets real deep really fast. For Rand the greatest conception of the human mind is, in fact, an abstraction, and elsewhere she will be more explicit about it. Fundamental to her position between Nietszche and Aristotle is in whose mind that abstraction belongs, man's or God's. I'll leave it there for now.