Linked by Thom Holwerda on Fri 22nd Mar 2013 10:02 UTC
"But a powerful new type of computer that is about to be commercially deployed by a major American military contractor is taking computing into the strange, subatomic realm of quantum mechanics. In that infinitesimal neighborhood, common sense logic no longer seems to apply. A one can be a one, or it can be a one and a zero and everything in between - all at the same time. [...] Now, Lockheed Martin - which bought an early version of such a computer from the Canadian company D-Wave Systems two years ago - is confident enough in the technology to upgrade it to commercial scale, becoming the first company to use quantum computing as part of its business." I always get a bit skeptical whenever I hear the words 'quantum computing', but according to NewScientist, this is pretty legit.
RE[4]: later
by Alfman on Sun 24th Mar 2013 20:53 UTC in reply to "RE[3]: later"

Member since:
2011-01-28

BeamishBoy,

"Infinity is a well-defined concept. It's so well defined that one can talk about (i) different kinds of infinity, and (ii) how one version of infinity is 'larger' than another."

I didn't say it wasn't a well defined concept. It's just that the concept is being abused when we treat infinity as a discrete number as though it could be compared.

"I know this stuff is confusing but it's been understood by mathematicians for over a century."

It's really not that confusing, if you attempt to solve a discrete number for "infinity", anyone else can conceive of a number a number which is factually higher, therefor the concept of infinity rules out the possibility of any discrete number equaling infinity.

What we can do is compare sums of series which approach infinity at different rates, like you did earlier. Discrete calculus (which as you noted is well understood) allows us to solve the rate for any given iteration of the sequence and confirm via inductive proofs that it continues infinitely.

There are an infinite number of unique sequences who's sums add up towards infinity given an infinite number of iterations. Because of the transitive properties of mathematical equality, one cannot claim any of these infinite sequence sums "equal infinity", for the simple reason that they are not equal to each other.

We might be careless and say a given sum "equals infinity" and still understand one another, but we don't actually mean it in the true mathematical sense.

This is what my earlier example was trying to illustrate. If infinity could be treated as a discrete number, then mathematically this would be sound:
A=infinity
B=infinity
B-A = 0

But in fact the earlier example showed that B-A=A.

To be sure, I am arguing semantics in the conversation as a whole and not just you. I don't want us to talk over each other, and I don't think we have all that much to disagree on, despite your bolded statement that "This is completely incorrect."

Edited 2013-03-24 20:57 UTC