Infinity: The Most Fascinating of All Ideas
This afternoon I enjoyed a great science lecture -- part of the Royal Canadian Institute's Science on Sundays in Toronto. The lectures are hosted every Sunday at University of Toronto's Macleod Auditorium, the Medical Sciences Building, at King's College Circle. Today's speaker was Miroslav Lovric of the Department of Mathematics and Statistics, McMaster University. His topic: Infinity: The Most Fascinating of All Ideas.
Lovric's a pretty good speaker, and did the topic justice in bringing it to a general audience. He stayed quite high level, and used a number of examples to illustrate inifinity's beauty, the paradoxes it raise and the importance of studying it. Goldbach's conjecture for instance, raised by Prussian mathematician Christian Goldbach in 1742, states that,
In discussing the topic of infinity, Lovric brought up a lot of topics that could all spawn their own lectures -- everything from mathematics, history and astrophysics. I've listed some of the more interesting topics below with links for exploration at your leisure. Infinity is fascinating, and Lovric's presentation will hopefully serve to whet a few appetites. I especially liked the Sanskrit description of infinity or asankhya he quoted:
Related links:
Lovric's a pretty good speaker, and did the topic justice in bringing it to a general audience. He stayed quite high level, and used a number of examples to illustrate inifinity's beauty, the paradoxes it raise and the importance of studying it. Goldbach's conjecture for instance, raised by Prussian mathematician Christian Goldbach in 1742, states that,
every even integer n greater than 2 is the sum of two prime numbers.Certainly, this may be just a mathematical exercise, but to date it still hasn't been proven, and not for the lack of trying. Some really bright minds were tested against this conjecture -- but for over 250 years, it has stood unproven. Xeno's paradoxes are equally illustrative of the power of infinity -- and great party tricks if you want to baffle some uninitiated minds. Of course, some of Xeno's paradoxes -- that of Achilles and the tortoise for instance -- remain unbroken for some time, until the mathematics was found that explained it (in this case, geometric series was needed). My favourite of Xeno's paradoxes is the arrow paradox, which essentially asserts that there is no such thing as motion. All really cool stuff -- and topics I encountered years ago in first year Calculus, but which has now faded somewhat with time.
In discussing the topic of infinity, Lovric brought up a lot of topics that could all spawn their own lectures -- everything from mathematics, history and astrophysics. I've listed some of the more interesting topics below with links for exploration at your leisure. Infinity is fascinating, and Lovric's presentation will hopefully serve to whet a few appetites. I especially liked the Sanskrit description of infinity or asankhya he quoted:
... the sum of all drops of rain, which, in 10,000 years, would fall on all the worlds.
Related links:
- Infinity -- Wikipedia serves up a good introduction to the topic. It's not necessarily for the layperson -- but read until you lose interest.
- Conceptual Metaphor and the Cognitive Foundations of Mathematics: Actual Infinity and Human Imagination [PDF] -- great paper by Rafael E. Núñez of the University of California.
- Continium hypothesis -- proposed by Georg Cantor in 1877, it introduces the concept of cardinality to compare the sizes of infinite sets.
- Brahmagupta -- an Indian mathematician and astronomer that lived between 598-668. Read the short reference in Wikipedia, especially if you, like me, got the Euro-centric history of the sciences when you were in school. [Check out Wikipedia's references to Ancient Mathematicians for more.]
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