Spacetime and the conservation laws

I'm reading Peter Atkins' book, Galileo's Finger, and in the chapter on energy, he makes the points that the conservation of momentum stems from the shape of space (that it's smooth and not lumpy) and that the conservation of energy stems from the shape of time (that it's smooth and not lumpy). I'm not totally clear on how the shape of spacetime leads to the conservation laws. Could someone elucidate the relationship, in layman's terms?

• John Reny's answer, is to the point. Shift symmetry of the space means that if a relation for a system is valid in $x$, is also valid if the system is shifted to $x+dx$, so having this symmetry and calculating the total momenutm of a system, it leads to $dp_{tot}/dt = 0$, which is the consnervation of momentum. Noethers theorem states that whenever a system has some symmetry another (associated) quantity is conserved. Whether this is a space property per se (and not a system property), is sth that can be debated. Jun 13, 2014 at 17:29