Related: Onsager received the 2000 Nobel Prize in Physics, also for 2D phase transitions. Trivia: Onsager was a Chemist! :D
EDIT: I believe this is the original paper: http://iopscience.iop.org/article/10.1088/0022-3719/6/7/010/...
Related: Onsager received the 2000 Nobel Prize in Physics, also for 2D phase transitions. Trivia: Onsager was a Chemist! :D
EDIT: I believe this is the original paper: http://iopscience.iop.org/article/10.1088/0022-3719/6/7/010/...
https://en.wikipedia.org/wiki/Kosterlitz%E2%80%93Thouless_tr...
And before anyone accuses me of wanting to dumb down Wikipedia: yes, that's exactly what I want. Wikipedia should be written to a generalist audience, not by specialists for specialists.
edit: I can't say it any better than this article: https://scholarlykitchen.sspnet.org/2012/09/24/wikipedias-wr...
And regarding wikipedia articles, there's two big design alternatives: for each article you either write into it all the necessary background, or instead link to the necessary background in different articles. I suspect that the modus operandi that wikipedia has chosen is that you should do the former for mainstream topics and the latter for niche topics.
I get the feeling that most math-involving Wikipedia pages are simply compound regurgitations of various textbooks.
> you need to learn a lot in order to even understand their starting point
This is kind of a cop-out. In the coming days there will be reams written on these laureates in the scientific press, much of which will be more enlightening, informative and contextually relevant than the dedicated encyclopaedia article.
You are absolutely right, because writing quality original work takes effort, and writing quality original maths work takes 100x more effort.
> This is kind of a cop-out
Call it whatever you want, but the fact remains that some subjects are more complex than others. Complex matters take more effort to write about, and there's fewer people qualified to write about them. When these two factors come together, you see regurgitated stuff. If you think that everything is equally simple if you explain it the right way, you're sorely mistaken about the nature of reality.
All this reminds me that I shouldn't be spending my own effort on HN :D
However, I must disagree with your claim that the scientific press will do better. As part of their coverage of the physiology prize they made up a new term "cell recycling" that will waste the readers time when they try to look up what it is about. As long as they are technically correct, the math wikipedia pages are at most useless.
https://en.wikipedia.org/w/index.php?title=Leaf&type=revision&diff=742673936&oldid=741796479
excising the hyperlink in the process.Your phrasing would be better were Wikipedia not a hyperlinked encyclopedia. Because Wikipedia is a hyperlinked encyclopedia, it's perfectly acceptable and even preferable to use stilted phrasing when it benefits the concise exposition of related concepts.
Archaic legal writing relied heavily on terms of art. Terms of art, IMHO, provided many benefits, including 1) concision, 2) consistency, and 3) signaling. Concision because terms of art are a way to reference more complex concepts that you don't need to spell out. Consistency because widespread use of terms of art meant that there was only one way to say something; if you used other phrasing it was presumed you meant something different than what was meant by a related term of art. And signaling because using a term of art made it clear and obvious you were referring to some concrete legal concept, even if the reader wasn't familiar with it.
Notably the shift to "plain language" legal writing did not in the least change expectations in the legal community regarding the consistency and signaling aspects of legal language. Today, instead of using terms of art, lawyers literally copy+paste whole blocks of long-winded clauses.
IMO, all three of those aspects--concision, consistency, and signaling--should likewise be emphasized in an encyclopedic text, _especially_ in the context of hyperlinked text.
Different contexts require using language differently. You wouldn't criticize a musician for using a different style of prose, right? It's not just the medium that dictates how we phrase things, but the context and function of the communication.
In my experience, the scientific press usually does not know what they are talking about, and relying on them for enlightenment or information is dangerous.
When you open a Wikipedia article about a complex subject, it's expected that you're going to do a lot of background reading.
The problem is that you start surfing Wikipedia with a BFS/DFS approach, when it would be a lot more efficient if the articles were organized more systematically to lead to a gradual understanding of the subject.
Until this has been done (feel free to help), I prefer that the specialists view is in place, rather than nothing. Or worse, a tabloid one sentence placeholder.
I don't see why this is a bad thing. I often do this for fun, and when I do it's never information I need to get on in my day to day life. These are extremely complex topics. If you don't want to understand them in their complete complexity, do you really want to understand them at all? What's the point of dumbing down a subject for the layman if the subject can't really be understood at that dumbness level?
My dream someday is to see these things organized into a "lattice", where links are clearly labeled as going "down" or "up" the lattice and you can have a clue what's going on.
An article like "Kosterlitz–Thouless transition" is not even being seen by a general audience anyways, except for when some news-worthy event like this happens, so why write like it's being read by someone it's not? It's not like writing this stuff is easy.
Obviously this is not exhaustive. But it gets you further than you naively think it should. Let's look at the harmonic oscillator, why is the thing probably a harmonic oscillator? Well the potential is typically an analytic function, and we are near a resting point, so the linear order in the Taylor expansion vanishes and the potential is approximately V(x) ~ x^2. Harmonic oscillator.
Say you want to look at a quantum field theory. Well actually defining one is hard. The only case where we know how to is for a free field theory. And a free field theory is actually a collection of harmonic oscillators.
Now interacting QFT, which underlies all of observed matter, is built by gluing together harmonic oscillators in a clever way. You know Feynman diagrams? The lines in a Feynman diagram represent the particle behaving as if it was made up of independent harmonic oscillators (free field). At the vertices we just bump the harmonic oscillators around a bit. So standard QFT is a very clever shuffling around of harmonic oscillators (lots of group representation theory organises the shuffling, and several Nobel prizes worth of physics are contained in the details).
Obviously there is plenty of physics that does not fit into either of these paradigms (GR, non-linear dynamical systems, atomic and molecular physics). But they both are utterly fundamental and enormously powerful tools in two very prominent branches in physics: High energy and condensed matter.
[1] https://en.wikipedia.org/wiki/Lars_Onsager
[2] http://www.nobelprize.org/nobel_prizes/chemistry/laureates/1...
Onsager wasn't alive in 2000.
If you want to get a start on understanding this, try considering the problem of BEC in 2D. The same logarithmic (algebraic, that is to say not exponential) divergence in that integral is at the heart of the BKT transition.