Note also that, even if these vessels were large enough to contain immense celestial hemispheres, both there upper edges and apexes of the cones therein contained would always remain equal and would vanish, the former into ‘round razors’ having the dimensions of the largest celestial orbits, the latter into single ‘points’. Hence, in conformity with the preceding we may say that all circumferences of circles, however different, are equal to each other, and are each equal to a single point.

And in answer to Euclid’s question of the ‘number of points in a line ?’ Galileo concludes:-

…..I shall ask you to tell me whether, in your opinion, a continuum is made up of a finite or of an infinite number of finite parts….My answer is that their number is both infinite and finite ; potentially infinite before division and actually finite after division ; because parts cannot be said to exist in a body which is not yet divided or at least marked out…..I think there is, between finite and infinite quantities, a third intermediate term which corresponds to every assigned number…..I grant, therefore to the philosophers, that the continuum contains as many finite parts as they please and I concede also that it contains them, either actually or potentially, as they may like…

Note also that, even if these vessels were large enough to contain immense celestial hemispheres, both there upper edges and apexes of the cones therein contained would always remain...

The real winds of change emanate from each individual citizen. It is we who have to think. To think whether it is necessary to make that trip or use that plastic bag, thus bringing...