What is infinity?
Image created by FAVIO.
Is the Universe finite or infinite? Is there infinity inside a black hole? Is space infinitely divisible or is there a shortest length? Can infinity occur at all in the cosmos or is it a mathematical construct? Find out more in our podcast with Anthony Aguirre, John D. Barrow and George Ellis. |
An infinite set is called countable if you can count it. In
other words, it's called countable if you can put its members into
one-to-one correspondence with the natural numbers 1, 2, 3, ... .
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Quantum mechanics and general relativity are incompatible — and this has led to a decades-long search for a theory of quantum gravity that could combine the two. But the particle physicist Richard Woodard thinks that the mismatch between the two could be nothing more than an illusion, created by the complicated maths techniques used in attempts to unite them. |
John Barrow gives us an overview, from Aristotle's ideas to Cantor's never-ending tower of mathematical infinities, and from shock waves to black holes. |
Infinity is a pain. Its paradoxes easily ensnare the unsuspecting
reasoner. So over the centuries,
mathematicians have carefully constructed
bulwarks against its predations.
But now cosmologists have developed
theories that put them squarely outside
the mathematicians' "green zone" of
safety.
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In the latest poll of our Science fiction, science fact project you told us that you wanted to know if infinity exists. In this interview the cosmologist John D. Barrow gives us an overview on the question, from Aristotle's ideas to Cantor's never-ending tower of mathematical infinities, and from shock waves to black holes. |
