Interesting Links for 17-07-2012
Jul. 17th, 2012 12:00 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
andrewducker- How Emma Sky went from anti-war academic to governor of one of Iraq's most volatile regions
- Screen Display Calculator - how far away should your TV be? And what size?
- Eight radical solutions to the childcare issue
- What did the Persians think of Alexander the Great?
- Free access to British scientific research within two years
- 7 reasons why I’m against DevoPlus / DevoMax
- Merely visiting a newspaper website can be a breach of copyright.
- How many infinities are there?
- The three options the Church Of England faces over same-sex marriage (well worth reading)
- Fifty Shades of Babe: Duke Nukem Reads E. L. James
- Facebook Engineer Responds to Imgur Block with Epic Reddit Apology
- US Security Agents At Heathrow For Olympics
Tags:
- calculator,
- childcare,
- children,
- churchofengland,
- copyright,
- dukenukem,
- epicwin #,
- facebook,
- funny,
- government,
- greece,
- history,
- images,
- independence,
- infinity,
- iraq,
- law,
- lgbt,
- links,
- marriage,
- middle_east,
- monitor,
- peace,
- persia,
- porn,
- reddit,
- religion,
- research,
- science,
- scotland,
- security,
- size,
- tv,
- uk,
- usa,
- video,
- war,
- wtf
![[identity profile]](https://www.dreamwidth.org/img/silk/identity/openid.png){kind=small}
no subject
Date: 2012-07-17 08:13 pm (UTC)How many infinities are there?
Date: 2012-07-17 11:33 am (UTC)(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.
For instance a number is often adjoined with a +INF and -INF which work roughly the way you'd expect (INF>x for any finite x; INF+x is INF for any finite X; INF-INF not defined). There are two of those. Eg. floating point representations on a computer often have somehting like this with a special bit pattern for results which are +INF, NAN, etc.
For complex numbers, there's only one INF, which is sort of "round the edge" of the whole plain.
Although obviously, if you lumped those in with the ordinals and cardinals, the answer would still be "too many to represent" :)
Re: How many infinities are there?
Date: 2012-07-17 12:06 pm (UTC)But everyone uses the normal one, and I don't think the alternatives have proposed anything significantly better.
no subject
Date: 2012-07-17 01:15 pm (UTC)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.
no subject
Date: 2012-07-17 01:26 pm (UTC)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.
no subject
Date: 2012-07-17 01:46 pm (UTC)The rationals are easy to label: have a table with the integers on top and side, generating rationals by top/side (and being sensible about 0), then move diagonally back and forth labelling all the numbers. There will be some overlap, but it's fine to give the same number two labels when it can be presented in two different ways. There are, however, only countably many rationals between any two numbers, not uncountably many.
The take home message remains that there are two types of infinity that should suit most people.
no subject
Date: 2012-07-17 02:10 pm (UTC)no subject
Date: 2012-07-17 02:20 pm (UTC)no subject
Date: 2012-07-17 02:22 pm (UTC)no subject
Date: 2012-07-17 03:39 pm (UTC):-)
no subject
Date: 2012-07-17 08:31 pm (UTC)no subject
Date: 2012-07-18 10:31 am (UTC)no subject
Date: 2012-07-18 10:39 am (UTC)no subject
Date: 2012-07-18 12:36 pm (UTC)no subject
Date: 2012-07-18 12:39 pm (UTC)no subject
Date: 2012-07-18 02:46 pm (UTC)Geeks FTW.
no subject
Date: 2012-07-18 05:57 pm (UTC)no subject
Date: 2012-07-17 05:47 pm (UTC)no subject
Date: 2012-07-17 08:30 pm (UTC)no subject
Date: 2012-07-17 09:36 pm (UTC)no subject
Date: 2012-07-19 10:07 am (UTC)no subject
Date: 2012-07-19 07:39 pm (UTC)(This glosses over some technical details about numbers with two binary representations but that doesn't make much difference)
Incidentally, Greg Egan once wrote a short story where it was critical to the plot that the Cantor set was uncountable. I'm pretty sure he did it to prove he could.
no subject
Date: 2012-07-19 11:20 pm (UTC)When it comes down to it the properties of the Cantor set are quite remarkable... measure zero, nowhere dense, a complete metric space yet uncountable. No wonder it gave mathematicians of the age fits!
I mentioned elsewhere (not sure if in reply to you) Rudy Rucker's book "White Light" which also hinges on the countable, uncountable and other possible forms of infinity.
no subject
Date: 2012-07-19 10:03 am (UTC)I would answer "there are *at least* two infinities" -- the ones you state (aleph nought and c). We do not know if aleph one is the same as c -- and it may require extra axioms in our chosen set theory.
http://en.wikipedia.org/wiki/Continuum_hypothesis
Incidentally, Rudy Rucker's terrific but weird "White Light or What Is Cantor's Continuum Problem?" addresses the issue in a scifi way with lots of drugs and giant talking cockroaches.
no subject
Date: 2012-07-17 12:56 pm (UTC)no subject
Date: 2012-07-17 06:14 pm (UTC)http://www.thedailybeast.com/newsweek/2011/07/17/marissa-mayer-on-the-internet.html
no subject
Date: 2012-07-17 08:30 pm (UTC)I've done somewhat similar things, although fortunately I don't have anything like that kind of effect when I do!
no subject
Date: 2012-07-18 07:19 am (UTC)no subject
Date: 2012-07-19 10:32 am (UTC)Let me start by saying that open access is a great thing. All my papers are freely available on my website and this is completely within publisher terms. I cannot remember the last time I came across a modern paper in my field which I had to go through a paywall for. The problem tends to occur with papers from five or more years ago when people were less savvy about putting things online. In some disciplines you are nowhere if your research is not also on arxiv which is completely free and open. Thanks to google, making a copy available on the web means that everyone can find it by searching the title. My webpage often has links to the "pay" version of the article too.
http://www.richardclegg.org/pubs/
e.g.
Elsevier pay version:
http://www.sciencedirect.com/science/article/pii/S002200001000111X
My free version
http://www.richardclegg.org/pubs/nsrl_jccs2009.pdf
This is entirely within Elsevier's rules.
It is what that article refers to as "green" open access.
You have to understand a little bit about how academics work to get some of the reasons why this "gold" open access a bad thing. There are so many papers coming out you can't read them all. In fact you can't read even an appreciable fraction in your field. In my field I can't even find time to read the top three journals and publication tends to be spread. Because network science is fast moving (and particular Internet science) we tend to track conferences not journals. Probably the most reputation making thing I can publish in (short of science or nature) is a conference (ACM SIGCOMM) -- not made it yet. If I publish in more minor venues or journals my work will not get read by the people I want it to get read by. So if I want my work to be out there I need to publish in certain places. If I am mandated only to publish in journals which will follow this "gold open access" cost model my work will not be so widely read. So this "free" access has a great danger of leading to UK research being ghettoised. It may be that leading journals will switch to allowing "open access for money upfront" but there's no guarantee they will.
There's a lot of "shock horror" 60% (perhaps more -- that's a figure I pulled from the air) of university library budgets go on journals. However, 99% of my library usage is on journals. That is pretty much the only use I make of my university library is to get papers and only then by the fact that accesses from inside my university "unlock" publisher paywalls. My access pattern is pretty typical (indeed, I'm more inclined to read a library book than most colleagues I think). So the high library expenditure on journals is actually under proportionate to what staff and postgrad students use -- and those are the majority users of the library. (The undergraduates are the ones there in person but that's not representative).
This proposal does not address the problem that academic publishing is profit driven because the same amount of money goes to the publishers, just by a different mechanism. So the publishers can still profiteer, they just do so by a different mechanism. (Incidentally, the "profiteering" Elsevier Reed sacked their CEO two or three years ago because of their low profits).
This problem will make things worse for non university people who wish to engage in science. A lot of people wish to publish without a formal connection to a university. (I gave the example of Einstein in the patent office -- a more common example would be a PhD student recently written up, a researcher between jobs or a retired professor who keeps coming up with good ideas). Now, what happens to their work. If the journal they want to publish in is a normal journal they're fine. If that journal is a "gold" open access journal then they've got a big problem.
Here's the real kicker though. Are the libraries going to stop paying Elsevier, Springer-Verlag et al? Of course not. Nowhere else in the world will do this "gold" open access. Any required journal subscriptions will still be required so the university will pay twice -- once to publish everything and once again to read it.
no subject
Date: 2012-07-19 10:43 am (UTC)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.
no subject
Date: 2012-07-19 10:50 am (UTC)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.
no subject
Date: 2012-07-19 10:58 am (UTC)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.
no subject
Date: 2012-07-19 11:03 am (UTC)