 About 91,700 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 Jeremy Gray  1999  289 pages In 1877 he wrote to his parents: The entire new mathematics (from about 1830 on
) is, I think. of no great value to the ... parts, that it no longer has anything in
common with reality; for instance, the nonEuclidean geometry, which is based
on the ... 

 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 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 The reader will, I trust, pardon its somewhat technical character, for without this
investigation of pointmotion it would be impossible to ... of other points or
geometrical bodies besides O which we wish to distinguish from P, and to do this
we. universe. The universe has been with ... properties, the carpenter makes for
us a box according to our geometrical description, but in reality not ultimately
geometrical. 

 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 Unless it has very peculiar properties, like discontinuities or restricted regions,
local geometry (that for just a small region) is almost determined, {{it is a manifold
}}. If coordinates are real it is Euclidean (flat); there is no remaining freedom (
except the dimension). And even ... Yet why is mathematics thus reality so limited
? 

 books.google.com In reality, both in the domain of geometry and in the domain of physics, infinity
has a distinctive meaning, which differs very greatly from the snictly mathematical
meaning. And the establishment of different meanings of infinity solves a number
... 

 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. 

 books.google.com However, modern cosmology has been possessed by the problems since its
birthm, and there were always new problems replacing old ones in its
development procedure. ... Therefore, the universal causal link in current
universe can not be explained clearly. ... But in reality, even one of them has not
been discovered! 

 