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Comment on "Research" by "Ian Durham

Ian Durham — Sep 30, 2008 - 7:20pm

Apparently not viewable yet, so I'll upload it here under my files as well.

Comment on "Research" by "Ian Durham

Ian Durham — Sep 30, 2008 - 7:18pm

OK, latest version now on arXiv. It includes the idea that the second law of thermodynamics is a boundary condition on classical knowledge.

Latex Test

Joe Fitzsimons — Aug 6, 2008 - 4:57pm

[tex]\ket{\alpha} \otimes X_i \ket{\beta^{(k)}_j[/tex]

Latex Support

Joe Fitzsimons — Aug 6, 2008 - 4:46pm

One feature that is definitely necessary to make this site useful to scientists is support for mathematical equations. There are several routes that could be taken to achieve this (i.e. MathML, LaTex, etc.) but I have decided that LaTeX support is the best solution. Anyone who needs to use equations witrh their work is almost definitely familiar with LaTeX syntax already, and my generating images of the equations it is possible to avoid the need for special plugins.

Progress

So far I have managed to install latex and ghostscript onto my webhost, which was no mean feat. Unfortunately I have discovered that the official Elgg LaTeX plugin is rubish. It appears only to support single line equations, and even then, only in blog posts. The blogs are intended merely as a way to point to places of interest, particularly within notebooks, and so this is rules out the official plugin.

I now have some shell scripts written which will convert a string into a PNG graphic of the equation, but I still need to actually implement the parsing and processing of content on the site. I'm not sure that this will be so easy as Elgg strips slashes from much of the input automatically.

Planned Features

Joe Fitzsimons — Aug 6, 2008 - 4:34pm

The features listed in this section are planned, and this is a way to keep track of my progress on them.

You can load a variety of files and online services (html) here.

Social Notebook Development

Joe Fitzsimons — Aug 6, 2008 - 4:32pm

I have been thinking what best I can use an open notebook for, and then it struck me: use it to plan out development of the site. Here I plan to keep track of the development. I do have a real job, though, so it might move slower than desired. Feel free to drop comments on any section with suggestions or feedback.

Comment on "Research" by "Ian Durham

Ian Durham — Aug 4, 2008 - 6:58pm

OK, my latest research idea that needs some work is something growing out of that paper on the Cerf-Adami inequalities that I'm still tweaking (with Terry Rudolph's help). There's presently a discussion of it, by the way, over at Quantalk.org (who reviewed an earlier version, pre-Terry). I'll post the latest version here in a bit. My idea is this: all forms of classical entropy essentially count things since, even though it is usually a unitless measure, we conventionally measure it in bits (in information theory). Thermodynamic entropy, when interpreted in the statistical mechanics manner (as a rescaling of the multiplicity), can also be thought of as counting something - and in fact can be converted to the "unitless" bits by dividing by Boltzmann's constant. So let's take a page from Cerf and Adami and think of entropy as simply counting the bits of information for a state. These bits represent a set. Entropy, then, counts these and is thus the cardinality of the given set. As you'll see in my paper that I'm going to upload in a moment, all the usual definitions of mutual, joint, and conditional entropy arise naturally from this interpretation (since it really is what Cerf and Adami were ultimately doing anyway, so this part, at least, just represents a clarification of their methods). Now, the interesting thing I was able to do in my paper was to use this to derive the Cerf-Adami inequalities without any reference - explicit or implicit - to Markov processes (which I also show are at least implicitly implied in at least one derivation). I also essentially propose a new way of looking at the second law of thermodynamics. So my next idea is that, if we want to extend this definition to von Neumann entropies, how do we do it since von Neumann entropies do not necessarily obey the CA inequalities? The thought I had was that classical entropies represent cardinalities of of *well-ordered* sets while von Neumann entropies do not. Hence the latter would simply be a generalization of the former. The question is: what else can be obtained from this interpretation? Is there anything else we can do that makes this useful?

Notebook

Ian Durham — Jul 20, 2008 - 10:23pm

Start your new notebook here!.

Research

Ian Durham — Jul 20, 2008 - 10:23pm

Use this area to describe your research.

You can load a variety of files and online services (html) here.

Notebook

Christopher Altman — Jul 15, 2008 - 6:34pm

Start your new notebook here!.