How many times have you been doing a literature search, found an article through searching on Google and then been frustrated that it costs 
10, $20, or more dollars to gain access to an article? I find this too often to be the case. Why? It shouldn’t be that way. I think that scientific knowledge should be freely available but with copyright protections to benefit the author (not the publisher!).
Lawrence Lessig from Harvard recently gave a talk at CERN about this very issue. I think this should be required viewing for all in academia. Here’s the talk:
I’m teaching E&M this semester, and the following question arose as I was preparing a lecture on the mathematics needed for studying electricity and magnetism. When one talks about the divergence of a vector field, it’s nice to give a physical picture of what 
means geometrically. The standard picture is that a vector field 
has a non-zero divergence if the vector field either emanates from (positive divergence) or converges (negative divergence) to a point. Like this positive divergence field:
This vector field has a positive divergence, and no, this is not the field I'm asking you to create.
In case you’re interested, this field is simply given by 
. So this is a nice picture to keep in mind, and it helps you see why the vector field 
has zero divergence:
This field has zero divergence. Can you see why?
Ok. Now you have a geometrical picture of divergence, right? Use this understanding to tell me whether the field below has a non-zero divergence:
Can you create an electric field like this?
In this case, the geometrical picture I painted for you doesn’t give the right answer. This vector field does not diverge from a point, as the field lines are all precisely parallel. However although, the field 
does not emanate from a point, it is always pointing away from the y-axis. Furthermore, the algebraic formulation of the divergence of this vector field is easily calculated:
![\[\vec{\nabla} \cdot \vec{v} = \frac{\partial v}{\partial x} = -\frac{1}{x^2}\]](http://www.paulnakroshis.net/blog/wp-content/ql-cache/quicklatex.com-7d52b8aae1257481e59205f3637e0ec6_l3.png "Rendered by QuickLaTeX.com")
and this divergence is always negative, at any value of x.
So my question is this: is it possible to create an electric field that has globally parallel electric field lines yet still possessing a non-zero divergence just like the plot above? If so, what charge distribution would give rise to such a field?
Does my geometrical picture of divergence need to be modified?
The author of the LaTeX plugin that I am using in this blog is thinking about scientific blogging and how to improve it. And a point he made to me in a recent email has stuck with me: Scientific blogs need to be able to be more interactive than standard blogs which can rely almost entirely on text and occasional images. It should be EASY for the author of a scientific blog to include content about their current research—this includes data, plots, and analysis. Ideally, such a blog could serve as a laboratory notebook as well as a blog.
Here’s a wish list of what I’d like to be able to do in a blog:
- Good typographical quality for text and mathematics— i.e. LaTeX output quality.
- The ability to export a blog entry automatically to a .tex file (or perhaps a pdf)
- The ability to do calculations and link to data files and plots
- The ability to do live animations
- Ideally open-source
I’m sure you can think of some more features that would be desirable, but the above five would be a good start. Several things strike me when I think about this list:
- Although it goes against my wish for an open source solution, I think Apple could really relatively easily satisfy my blogging needs with an update to iWeb. iWeb is very easy to use, and makes it trivial to include text, images, and movies, as well as making linking to files rather trivial. However, it needs better web standards compliance, the ability to incorporate mathematics, and to be able to do calculations. Does anyone at Apple think about incorporating these things? Maybe as a new application: iWebScience?
- Here’s another thought: the application SAGE (google it!) is a python-based mathematics program that aims to include Mathematica-like capability and python programmability (including Matplotlib graphics) all in one unified notebook interface that runs in a browser. All we need is someone to write a beautiful plugin for either WordPress (to use SAGE) or a plugin for SAGE to allow blogging.
Do you have other ideas? I don’t see any science blogs that satisfy all my criteria yet; it’s an area of web publishing that I’d like to see expanded. And if you haven’t seen or used SAGE yet, you owe it to yourself to check it out.
My idea with this site (at least initially) was to be able to have a convenient place to write thoughts and include data—a somewhat reasonable attempt at having a laboratory notebook online. One of the impediments that I’ve always had with this is that writing about physics invariably involves the need for mathematical typesetting ability, and that is not something I was aware of how to do until I thought to check the WordPress plugins and search for LaTeX. After reading lots of reviews, I settled on QuickLaTeX, and I’m giving it a hearty try. I also wanted to have a nice clean layout for my page, and settled on this Manifest theme (see bottom of page for a link). Together, I think these two look beautiful.
Ok, but here’s my gripe, and it comes with a question, then a plea. The gripe is that to see the form of my output, I have to preview it, and that preview is SLOW, painfully slow (on my admittedly 4 year old MacBook Pro), and I think that’s unfortunate. But I have an idea for a fix, a wonderful one if it could be done! Of course, anyone that uses LaTeX is likely familiar with TeXShop (by Richard Koch) or its cross-platform clone TeXWorks…wouldn’t it be nice for the QuickLaTeX Developer Pavel Holoborodko and the WordPress team to talk about a way to have a TeXShop like interface in the WordPress Editor Window? Imagine being able to do that and have an instant preview available. Wow.
The question is….can this be done in WordPress? If not, is there any blogging platform that does?
If it can be done in WordPress, could someone pleeeeze implement that? If we had that capability scientific blogging would be quite a pleasant affair. While your at it, could you engineer in a feature that would automatically email a .tex file of each complete blog entry to your email account? That would be a nice addition.
So, any volunteers? Pleeze….
My student (Cody Goolsby) and I are building a torsion pendulum magnetometer to monitor the earth’s magnetic field . We’re using a 40 micron diameter gold-plated tungsten fiber that will be about 100 cm in length. The torsion constant will then be approximately
![\[ \kappa = \mu\frac{\pi r^4}{2 L} \;\sim \; 0.40\; \mathrm{dyne\cdot cm/rad}, \]](http://www.paulnakroshis.net/blog/wp-content/ql-cache/quicklatex.com-3ff48cc1036b1300da78a27e3952bbac_l3.png "Rendered by QuickLaTeX.com")
where I’ve used the value of 161 
for the shear modulus of tungsten. Hmmm, Quick, the LaTeX code wasn’t rendered properly in the last sentence…
Update: Miraculously, the creator of QuickLaTeX emailed me to let me know he’d fixed the problem! (As you can see, the equation now renders fine…)
Here’s my first attempt at an electronic laboratory notebook. I still like paper (a lot actually!), but I’m experimenting with an online notebook, and I thought I’d give WordPress a whirl. I’ve installed the QuickLaTeX plugin so that I can type mathematics, so we’ll see how it goes.
Here is an equation:
![\[ \int_0^3\; x^2\;dx \]](http://www.paulnakroshis.net/blog/wp-content/ql-cache/quicklatex.com-024a954c2ffb6d47a8f8bc71b0e46af5_l3.png "Rendered by QuickLaTeX.com")
See, it works!
