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The word 'infinity' refers to a few different concepts in different branches of mathematics. Some of them have been well-defined and well-understood for a long
by lmkg 10y ago
The word 'infinity' refers to a few different concepts in different branches of mathematics. Some of them have been well-defined and well-understood for a long time. The point named "Infinity" as a limit in analysis/topology (which I think is what renormalization is related to) is very un-mysterious.
Cantor's work in the early 20th century was on infinite objects in the context of set theory. That work is also fairly well-understood but starts to get a bit esoteric. More recent research goes further in the same direction, and then you start getting the point where you can't prove whether a certain type of infinity exists or not, because the existence of an infinity that large would prove that set theory is consistent.
So yes, research is still ongoing into the nature of infinity, but it's the nature of a different infinity.
- mindcrime 10y agoFair enough. Like I said, IANAM. I just enjoy reading books like Everything and More: A Compact History of Infinity and Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World. It's certainly a wildly fascinating topic.
- vanderZwan 10y agoIs this related to that whole -1/12 business, which they talk about in this Numberphile video[0]? Because the video suggests it's ongoing work in mathematics and that it shows up in unexpected places in theoretical physics. [0] https://www.youtube.com/watch?v=0Oazb7IWzbA https://www.youtube.com/watch?v=0Oazb7IWzbA
- gohrt 10y agoThe Numerphile video has been debunked by everyone else in the math-popularization community: http://blogs.scientificamerican.com/roots-of-unity/does-123-really-equal-112/ http://blogs.scientificamerican.com/roots-of-unity/does-123-... (and also see discussion of that article on HN The "-1/12" "mystery" is well settled math (but mathematicians are always looking for more elegant or general perspectives on things), and (standard-issue) sloppy notation in physics. The only "mystery" is why people who should know better intentionally use incorrect terminology to dazzle lay-people, creating a mystery where there is none.
- vanderZwan 10y agoThanks for that follow-up!