After the readings on Non-Euclidean
Geometry, a few things stuck out to me. The creation of non-Euclidean geometry
came from trying to prove something the parallel axiom. How this mathematical
advancement came out of actually trying to prove something to be correct, and
ultimately not being able too.
Again I find it interesting how humans react to problems, we immediately
to try to solve them rather then bringing up the possibility that they may be
wrong. Individuals spent their live trying to prove Euclidean’s parallel axiom
was true; Hume was one of the only ones to express a little doubt. Everyone
else was trying to prove that this axiom existed. Ptomey was the first, next
Proclus; then another long list of individuals spent their lives trying to
prove the parallel axiom. They were all using an inductive method, once they
weren’t able to prove it that way, another group switched to try to prove it
through deduction. At the end, all
of these individuals were using the previous knowledge that other had discovered
and Gauss was labeled the creator of non-Euclidean geometry. I thought it was
interesting that Gauss the name changed the name of the geometry three times
until he chose non-Euclidean. I wonder about this, was there some reason behind
this? Or am I simply focusing on a fact that isn’t important?
The fact that we can label different creators was also brought up in the first article from chapter 36, defending that Gauss as
the creator, because the most significant part was not needed for mathematical
development. Stating how Lobatchevskey and Bolyai learned the ideas from their
teachers who learned it from Gauss. In the other article there was opposing
views, and stated that Lobatchevskey, Bolyai and Riemann were the creators of
this geometry that had the greatest advancement since the Greeks. I find it
interesting that they have opposing views on the creators, and important
influences in this new geometry. Looking at the creation of non-Euclidean
geometry do you agree that the most important fact is the development of the
properties of physical space? Can there be one person who could have been the
“liberator” of math?
Abbie, your question about the properties of physical space got me thinking. What is physical space? While my understanding of the competing views is elementary, I believe I understand that there were two views of space given in the reading: (1) an objective space, or the reality that exists for us to "play in," demonstrated by Euclidean Geometry; and (2) a subjective collection of relations in which we give meaning.
ReplyDeleteKline differentiates between these two versions of space when he talks about mathematics. He asks that when a mathematician comes up with a theory: is he/she unearthing an innate relationship (characteristic of space (1), a self-substitive reality) or synthesizing a relation between two unrelated things (characteristic of space 2).
Bernoulli's principle of lg #'s seems to advocate for space (1), while Hume argues for space (2). My point is that the answer of what space is for us is an important axiom for deciding the debate on the ultimate reality of math as an ultimate truth of nature.
You know Abbie, if there is one thing this class has taught me, there is no "one person" who can be called the "liberator, founder, or creator" of any field of mathematics. This article, like most of Klien's articles that we have read, shows just how the people who are attributed with discovering something actually got their inspiration from someone else. There are a select few who have may have made bigger strides then others, but in the end the whole field of math is a long evolution of thoughts that can't be pinpointed to just one person. This all just goes back to what Dr. Crist was saying in class about our western philosophy is turn people into heroes.
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