Infinity. It’s a puzzling concept. Is it real, or a mathematical fiction?
Aristotle believed infinity could only be potential, never actual. To speak of an actual infinity, he argued, is to fall into logical contradiction: “The infinite turns out to be the contrary of what it is said to be,” Aristotle wrote in the Physics. “It is not what has nothing outside it that is infinite, but what always has something outside it.”
Aristotle’s logic rested on common sense: the belief that the whole is always greater than the part. But in the late 19th Century, Georg Cantor and Richard Dedekind turned common sense upside down by demonstrating that the part can be equal to the whole. Cantor went on to show that there are many orders of infinity–indeed, an infinity of infinities.
But what relation does the Platonic realm of pure mathematics have to the physical world? Physics is an empirical science, but that hasn’t stopped theorists from imagining the mind-boggling consequences of an infinite universe. To Infinity and Beyond, a one-hour BBC Horizon special featuring interviews with leading mathematicians and physicists, is an entertaining exploration of a subject which, by definition, you won’t be able to wrap your mind around.
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I usually like your suggestions, but this documentary is terrible. Did you actually watch it before recommending it?
I suppose I can see where you’re coming from, José. The narration is melodramatic, and I have to admit I was a bit annoyed by all the counting aloud (“googolplexplexplex five, googolplexplexplex six…”). But they interview some very interesting people. And the subject is certainly fascinating. So…
Best,
Mike
This is a ridiculous “documentary.” The only thing I really took away from this is that infinity is whatever you want it to be.
This was rubbish. Low grade self indulgent film making. Most of the comments on Youtube say the same.
It is interesting to see that some people are not familiar with real artistic craftmanship. The BBC makers actually made an effort to go beyond boring hyperbolic docu’s making with a drumbeat of facts and finish with an exact punchline.
For instance, the melodramatic scenes give this abstract subject much needed feeling. Why would Cantor otherwise have gone mad? I love also the child interviews where some of the kids really think they know the biggest number. How great to have that certainty for some time..
For that reason, I would consider also commentator Z here above simply a Zeilberger. The documentary has explained some limits on infinity, but If you don’t like the concept, no documentary is going to help you there.
I disagree in some points:
Infinite is the total of all. You cannnot add 1 to infinite because it’s already there.
The hotel example was very weird.
How could it be possible infinite – infinite = infinite? It’s simple:
infinite = infinte, so, infinite-infinite=0.
Period.
Infinite is absolute and has no end neihter start.
So the infinite symbol is wrong, it represents a course that ends and starts in itself.
Just talking…
by the way…interesting doc
The first 10 minutes were a total waste of time. It might have improved later, but I doubt it. Avoid.