 About 33,300 results  books.google.com However, this is only because space is insubstantial, not because it has no
physical reality of its own as relationism ... of the Universe having either curved or
flat space depends to a great deal on the accuracy of geometry in describing
reality. 

 books.google.com Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a ... 

 books.google.com It then becomes hard to understand how anyone could argue that the matter is
primary to the geometry that constrains it. ... useful for predicting waves, or
orbitals, at different energy levels and quantum states, but it has no explanatory
power. ... In this new interpretation of quantum theory, reality is not seen as fuzzy,
probabilistic, or nondeterministic, since such terms have no meaning when
applied to the ... 

 books.google.com 
 books.google.com Here we must consider the expanse of the universe to determine whether it
embraces anything infinitely large. But here again modern science, in particular
astronomy, has reopened the question and is endeavoring to solve it, not by the
defective means of metaphysical speculation, but by reasons which are based on
experiment and ... Although euclidean geometry is indeed a consistent
conceptual system, it does not thereby follow that euclidean geometry actually
holds in reality. 

 books.google.com Whereas a triangle in reality would have to be put together materially and could
break, sag, or wear out, the triangle of geometry, after possibly being drawn by a
pencil, is nevertheless visualized as having sides and dimensions that do not ... 

 books.google.com This view seems to be based on the hope that someday a universal law will be
discovered that says there is no law. ... is not an explanation, but an evasion, an
escape from the reality that there is much about reality that cannot have an
explanation. ... Their properties are purely consequences of geometry — which
has nothing to do with whether the universe has structures and nothing to do with
life. 

 books.google.com For Plato, as for the followers of Pythagoras some nine centuries earlier,
geometry was not simply a means toward practical ends. ... of geometrical reality,
in so doing he would touch near the heart of the universe, brushing against a
reality that is deeper than the reality we usually know. ... Or as Socrates put it in
Plato's Republic, “The man whose mind is truly fixed on external realities has no
leisure to turn ... 

 books.google.com Mathematics is indifferent to the application of its laws to things in reality, and its
axioms contain only a system of rules, ... Pure mathematical axiomatization leads
in no way to principles of a theory of natural knowledge. ... it takes away from
mathematics the question of the validity of geometry and has referred it to physics
. 

 books.google.com In our time, WMAP has proven that the geometry of space is “flat,” or “noncurved”
(we live in a Euclidean spacetime), and it has been flat since the first fragment of
time. ... ultimate destiny of spacetime, provided that the equations contained all
the necessary constraints that exist in reality. ... and that they could justify the idea
that space is infinite and the universe has no center, no edge, and no boundary. 

 