Interesting Links for 17-07-2012

[andrewducker]

• How Emma Sky went from anti-war academic to governor of one of Iraq's most volatile regions
  (tags: iraq war peace )
• Screen Display Calculator - how far away should your TV be? And what size?
  (tags: tv monitor size calculator )
• Eight radical solutions to the childcare issue
  (tags: childcare children government )
• What did the Persians

Comments

How many infinities are there?

[cartesiandaemon]

ROFL. That's really well written. I guess one might guess the answer is "infinitely many!" but it's good to see it explained.

(And as far as I can tell accurate: it's scary to think that now I know fewer practicing mathematicians, I probably know more about infinities than almost all of my friends :))

For the record, "infinity" is more of a label mathematicians and non-mathematicians slap on stuff which is "too big to count", so it usually means ordinals and cardinals, but there are some other uses

Re: How many infinities are there?

[cartesiandaemon]

And also for the record, there are alternative formulations of set theory where you don't have to put up with the "proper classes are things which are exactly like sets, but are not sets because that would cause paradoxes" stuff, but you have to give up something else you would expect (eg. the ability to say "the set of all elements of set x which are 'some property'")

But everyone uses the normal one, and I don't think the alternatives have proposed anything significantly better.

[spacelem]

If I were writing an essay about infinity, I'd say that while there are a lot of infinities, there are really only two kinds of infinity that you need to worry about: countable and uncountable.

Countable infinity is when you can order all the items in a set and label them 1,2,3,.... . You'll never end (obviously, because there are infinitely many of them), but every item in that set has a label. The set of integers is of this sort, because every integer has a name. We call this infinity aleph-null (א0).

Uncountable infinity is when you can't do that, because there are too many elements -- it's not clear what label something should have. For example, 0.999... with countably many 9s is exactly equal to 1, so two numbers with different labels are the same. What's more, is that with uncountable infinity, no matter how close two numbers, there are an uncountably infinite number of numbers between them. This is true of real numbers.

I think that's a rather more useful explanation of infinity, even if incomplete.

[khoth]

Your examples there aren't great - the rational numbers have both the things you cite for uncountable infinity: Labels aren't unique, eg 1/2 = 2/4, and between any two rational numbers there are an infinite number of other rational numbers. But the rational numbers are countable.

The thing with labels isn't to do with something having more than one label, it's about there not being enough *finite* labels to include everything. So 0.999.... isn't even acceptable as a label. The problem with real numbers is that there are uncountably many of them that just go on and on with no actual pattern, so you can't describe precisely what they are.

[ashfae]

I've missed the niftiness of the Screen Display Calculator to fall in smit with the Do What the Fuck You Want To Public Licence down at the bottom. Joy!

[ckd]

That imgur block reminds me of this story (with a name that's rather familiar lately in the tech news ;-) :
http://www.thedailybeast.com/newsweek/2011/07/17/marissa-mayer-on-the-internet.html

[andrewducker]

That's a great story.

I've done somewhat similar things, although fortunately I don't have anything like that kind of effect when I do!

[anef]

Somewhat at a tangent to the Alexander story, I can recommend reading "Persian Fire", by Tom Holland, which gives a fascinating overview of the older civilisations of the Middle East, and "The Crusades Through Arab Eyes", by Amin Maalouf, which is again fascinating, and does what it says on the tin.

[steer]

OK... I wanted to make a more coherent comment than twitter allows about this "gold open access

[andrewducker]

We're not the only people requiring open access. If you get money from the NIH in the US then you have to submit your paper to PubMed Central. Not quite the same, but enforcing open access for papers produced with public money seems to be slowly catching on.

I'm happy to accept that things are better than they were five years ago (which is when I was last hanging out with academics - who were in favour of open access). But the point you give about Einstein is easily reversed - with open access today's Einsten can read any papers they want to, rather than having to be part of a university to have those fees paid for them.

[steer]

However, as I argued, Einstein today can already read most papers in most fields anyway.

If you get money from the NIH in the US then you have to submit your paper to PubMed Central

I'm fairly sure that is a green not a gold model of open access. You publish the paper in the journal then you additionally make it open in pubmed central. Brilliant. I am completely in favour. Unfortunately, some publishers insist on a six month delay between publication and pubmed central so it's not quite as good as putting the paper on arxiv or your own website... but that is exactly the way open access should be. It's not what we would be getting in the UK though.

[andrewducker]

You're right - I went and did some digging, and found this:
http://romeo.jiscinvolve.org/wp/2011/11/24/60-of-journals-allow-immediate-archiving-of-peer-reviewed-articles-but-it-gets-much-much-better/

Which shows that over 80% of articles can be self-archived immediately, and it goes up to about 95% after embargos are over (typically a year).

Ok, you've sold me, this seems to be largely a solved problem, with only a small proportion of holdouts.