  Part 1 : For more than two millennia, ever since Euclid's geometry, the so
called Archimedean Axiom has been accepted without sufficiently explicit
awareness of that fact. The effect has been a severe restriction of our views
of space-time, a restriction which above all affects Physics. Here it is argued
that, ever since the invention of Calculus by Newton, we may actually have {\it
empirical evidence} that time, and thus space as well, are not Archimedean.
  Part 2 : There is an insufficient awareness about the {\it rich and complex}
structure of various totally ordered scalar fields obtained through the {\it
ultrapower} construction. This rich and complex structure comes from the
presence of {\it infinitesimals} in such fields, presence which leads to the
fact that such fields are {\it non-Archimedean}. Here, with the concept of {\it
walkable world}, which has highly intuitive and pragmatic geometric meaning,
the mentioned rich and complex structure is illustrated. The issues presented
have relevance for what are usually called the "infinities in physics".

General Mathematics