infinity_2011_upg
infinity_2011_upg,
"The Capture of Infinity",
about Cantor's theory of infinity,
given to the Student Mathematics Club
at the University of Pittsburgh/Greensburg,
07 December 2011.
I first planned to give this talk to the
undergraduate math club at the University of Pittsburgh, Greensburg (UPG),
during a visit in November 2009, but my schedule didn't work out.
I kept working on the talk with a view to a February workshop
at Virginia Tech, to be associated with the Center for Talented
Youth, (run through Johns Hopkins University), which would have
involved an audience of sixth graders and their parents (!).
The idea of having to speak about serious mathematics to such
an audience suggested more strongly that I should keep working
on the topic of infinity, an engaging subject whose paradoxes
can be understood without a great deal of prerequisites.
Alas, the CTY workshop was cancelled. I finally was able to
give the talk at UPG after all, on 07 December 2011.
The following files were used:
-
achilles.png,
an image of Achilles running, illustrating one of Zeno's paradoxes.
-
cantor.png,
an image of Georg Gantor, who developed set theory, and then
consistent and convincing theories of infinite cardinal numbers (which
measure size) and infinite ordinal numbers (which record order).
-
euclid.png,
whose proof of that there is no largest prime established a pattern
of argument repeated through mathematical history, and which also
showed that infinite objects existed, even if we refused to actually
consider them directly.
-
fourier_equation.png,
an image of a very simple oscillatory function, suggesting the
many zeroes such a function can have.
-
fsu_logo.pdf,
a logo.
-
galileo.png,
an image of Galileo Galilei, one of the first to consider
a paradox of infinity and have something insightful to say about it.
-
nail.png,
an image of a nail, suggesting a finite 1D line segment that
can be "rearranged" to form the Titanic.
-
quadratic_equations.png,
an image of some quadratic equations with just a few zeroes.
-
rationals.png,
an image of a table that suggests how all the (positive) fractions
can be counted.
-
sheep.png,
an image that suggests counting sheep.
-
stairway_to_heaven.png,
an image of a "stairway to heaven", suggesting the
endless series of infinities that Cantor uncovered.
-
titanic.png,
an image of the Titanic, a big 3D object that has no more points than
a 1 inch line segment.
-
wooden_blocks.png,
an image of wooden blocks forming a cube, suggesting how Albert of
Saxony's infinite beam could be rearranged to fill space.
-
zeno.png,
an image of Zeno, poser of several paradoxes.
Last revised on 04 February 2024.