Midpoint Quotes

Imagine we could accelerate continuously at 1 g-what we're comfortable with on good old terra firma-to the midpoint of our voyage, and decelerate continuously at 1 g until we arrive at our destination. It would take a day to get to Mars, a week and a half to Pluto, a year to the Oort Cloud, and a few years to the nearest stars. (Carl Sagan)
It has been a long road from Plato's Meno to the present, but it is perhaps encouraging that most of the progress along that road has been made since the turn of the twentieth century, and a large fraction of it since the midpoint of the century. Thought was still wholly intangible and ineffable until modern formal logic interpreted it as the manipulation of formal tokens. And it seemed still to inhabit mainly the heaven of Platonic ideals, or the equally obscure spaces of the human mind, until computers taught us how symbols could be processed by machines. View quote
Allen Newell
The classic instrument to measure drawn angles and to draw angles of a given measure is the protractor - essentially half a circular ring, subdivided by ray segments into 180 degrees. For reasons I was unable to find out, this instrument has recently been superseded by an isosceles right triangle - called geo-triangle, solid, transparant, made of plastic - with an angular division radiating from the midpoint of the hypotenuse to the other sides. Well, inside the triangle half a circle with the midpoint of the hypotenuse as its centre is indicated, and from the position of the degree numbers it becomes clear that it is the semicircle that really matters. One is inclined to say "an outrageously misleading instrument"... View quote
Hans Freudenthal