Review: SolydXK 2013.04.06

I originally wanted to do this one before final exams, but other hiccups in this review pushed that to now. Anyway, here it is.

Main Screen + KDE Kickoff Menu

What is SolydXK? Debian-based Linux Mint never had a KDE edition, so SolydK was born out of the unofficial project featuring KDE in Debian-based Linux Mint. Then, Linux Mint pushed its Xfce edition back to an Ubuntu base, necessitating the emergence of SolydX. Together they form SolydXK, based on Debian Testing but with update packs, just as Debian-based Linux Mint is.

I tried SolydXK on separate partitions of a live USB with UnetBootin, as MultiSystem did not recognize SolydXK (and that's why I was having trouble doing this review before final exams). Follow the jump to see what they are like.

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Featured Comments: Week of 2013 May 26

I was out of town over the long weekend, so I couldn't post this yesterday. There was one post that got a couple of comments last week, so I will repost both of those.

Review: Korora 18 "Flo" KDE

An anonymous reader asked, "do you have a review for gnome edition"?
Another anonymous commenter shared, "I've been running Korora 18 for a few weeks now. It's extremely polished and I had none of the errors you encountered setting it up. Everything just works for me."

Thanks to both of those people for commenting on that post. This coming week, I will have at least one review coming up, as I am at home now and will have some time to do this again. Anyway, if you like what I write, please continue subscribing and commenting!

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Done with 6th Semester!

I'm done with junior year! The spring semester was a bit more manageable than the fall semester, but was still challenging nevertheless. I intentionally chose to take only 3 classes: 8.06 — Quantum Physics III, 8.14 — Experimental Physics II, and 14.03 — Microeconomic Theory and Public Policy. I did this so that I could spend more time on each of those classes (especially 8.14 — Experimental Physics II) as well as on my UROP. Speaking of my UROP, things were progressing rather slowly in the beginning of the semester and only slowed further from there, until just after spring break, at which point progress went extremely quickly. I'm really looking forward to being able to make more such progress in the summer; plus, I may even be able to start on a new project about the Casimir effect, about which I wrote a paper for 8.06 — Quantum Physics III. Before that, I'm spending two weeks at home. For these next few days, I'm just going to relax and spend time and travel with family. After that, I'll probably be able to start work again on my UROP; a few weeks into the summer, I intend to start looking seriously into graduate programs in physics. Anyway, at last, it is summer!

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Review: Korora 18 "Flo" KDE

Main Screen + Kickoff Menu

In the last week of classes, since finished all of my assignments, I have had a little time to do some distribution reviews before starting to prepare for final exams. The second such review is of the KDE edition of Korora 18 "Flo".

I have reviewed Korora before. Back then it was called Kororaa (with an extra 'a'), so I guess the name was shortened in a manner similar to that of Facebook (from "TheFacebook"). It's a distribution that essentially offers a bunch of niceties on top of Fedora with GNOME or KDE. This time I tried just the KDE version.

I tried this as a live USB system made with UnetBootin, as making it with MultiSystem gave problems on several occasions. Follow the jump to see what it's like.

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Featured Comments: Week of 2013 May 12

There was one post this past week that got a handful of comments, so I will repost most of those. Also, I should mention that despite that post being a very short review-esque update, it somehow managed to get several thousands of views more quickly than any other post. I'd be curious to know where a lot of those views came from.

Review: CrunchBang ("#!") Linux 11 "Waldorf"

Reader DarkDuck shared, "I would not recommend #! to newbies. It's still to rough. But as soon as you become comfortable with the Linux system architecture and approach, #! maybe a good alternative. My own review of #!: http://linuxblog.darkduck.com/2012/03/crunchbang-linux-good-system-for.html".
Commenter krpalospo had the following question: "I really like debian, it was my first distro, but i have a question this distribution has support for apt-repository like ubuntu's distros the main reason for no using debian right now it's that this ubuntu tools help a lot in configuration of package system".
Reader Wolf had this to say: "Nice small delta review. I might try it someday, although I'm usually happy with Ubuntu LTS releases. One small thing: you may find even with error bars that 148 MB steady state RAM used is significantly different than the 150 MB steady state of before, but I question the practicality of this difference. 2 megabytes shaved off of steady state seems, practically, insignificant. I mean we are regularly seeing 32 and 64 GB RAM machines now, with 128 GB, 256 GB and higher on the high end. 2 MB steady state saved is miniscule."
An anonymous commenter asked, "Why isn't Semplice getting the attention it deserves. Imho it is better than #!, Been running it for a couple of weeks now and it a lot more polished than Crunchbang. Give Semplice a try."

Thanks to all those who commented on that post. This coming week, I have final exams and then I will be traveling home. My final exams go until (and include) Wednesday, so I won't really be able to write anything new for the week. However, I do have an already-written review on hold to publish this week. Also, I'll probably put out a post concerning the semester that is almost completed. Anyway, if you like what I write, please keep on subscribing and commenting!

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Review: CrunchBang ("#!") Linux 11 "Waldorf"

Main Screen + Openbox Menu

This is the last week of classes for me. I have turned in all my assignments and a handful of days until finals, so I can take today and tomorrow to write a couple of reviews at my leisure. The first will be #!.

#! should be familiar to many readers here. It is a lightweight Debian-based distribution that uses Openbox. While it is not technically a rolling-release distribution because it is pinned to the stable release, there were tons of preview releases for this version. Now that Debian 7 "Wheezy" is finally stable, so is #! 11 "Waldorf". Since version 10 "Statler", the Xfce edition has been dropped, so #! is back to using Openbox exclusively.

I tried this on a live USB made with MultiSystem. Follow the jump to see what it's like.

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Expected Utility in Quantum States

Last semester, 14.04 — Intermediate Microeconomic Theory covered choice theory under uncertainty; at the same time, I was taking 8.05 — Quantum Physics II, where we had talked about 2-state systems and the formalism of quantum states being complex vectors in a Hilbert space, and as choice under uncertainty discusses how consumers make choices based on states of the world, I thought it would be cool to extend it to quantum states, but I wasn't sure how to do that at that time. Now that 14.03 — Microeconomic Theory and Public Policy is talking about choice under uncertainty as well this semester, and now that I have had some time for the stuff about 2-state systems to simmer in my head, I think I have a slightly better idea of how to think about extended the states of the world to include the superpositions as allowed by quantum mechanics.

One of the simplest examples would be the 2-state system. In the class I am taking now, a typical 2-state system would be a fair coin which can either take on values of heads or tails (each with probability $\frac{1}{2}$). What might this look like in quantum mechanics? We could replace the coin with the spin $S_z$ of an electron. A state of the electron corresponding to being measured as $|\uparrow_z \rangle$ or $|\downarrow_z \rangle$ each with equal probability could be labeled as $|\psi \rangle = \frac{1}{\sqrt{2}} \left(|\uparrow_z \rangle + |\downarrow_z \rangle\right)$. This indeed gives equal probabilities of being measured as spin-up or spin-down in the $z$-direction. The problem is that this state is exactly $|\psi \rangle = |\uparrow_x \rangle$, so the probability of the state being measured in the $x$-direction as spin-up is unity. This leads to issues in trying to reconcile the interpretation of payoffs for different states of the world; this particular state would pay $w(|\uparrow_z \rangle)$ or $w(|\downarrow_z \rangle)$ with equal probabilities until $S_z$ is measured, but would pay $w(|\uparrow_x \rangle)$ with certainty as $S_x$ has essentially already been measured, collapsing a previously unknown state into this one. So there seems to be an issue with trying to stuff the interpretation of probabilistic measurement of a state of the world into the idea of superposing quantum states, as certain measurable states of the world do not commute ($[S_i, S_j] = i\hbar \epsilon_{ijk} S_k$ for instance). So what can be done now?

Recall that each state of the world $j$ has an associated probability $\mathbb{P}_j$. Yet, once a state is measured, those probabilities are meaningless, because a state becomes observed or not observed; it cannot be "observed in fraction $\mathbb{P}_j$" or anything like that. Taking the frequentist view, these probabilities are only meaningful in the large ensemble limit; after a large number of observations, the fraction of those observations corresponding to the state $j$ converges to $\mathbb{P}_j$. This is exactly the same rationale behind the density matrix, which describes the state of an ensemble of systems which are usually not all prepared in the same quantum state, but in the large number limit, the fraction of those prepared in the state $|\psi_j \rangle$ is $\mathbb{P}_j$ such that $\sum_j \mathbb{P}_j = 1$. It is then defined as \[ \rho = \sum_j \mathbb{P}_j |\psi_j \rangle \langle \psi_j | . \] Note that in general $\langle \psi_j | \psi_{j'} \rangle \neq \delta_{jj'}$ because the states do not in general need to be orthogonal. Furthermore, different state preparations can have the same density matrix, in which case the "different" state preparations are actually physically indistinguishable if a quantum mechanical measurement is made.

So what does this have to do with the states of the world? If the example of a fair coin flip is again translated into measuring each eigenvalue of $S_z$ with equal probability, then the density matrix becomes $\rho = \frac{1}{2} \left(|\uparrow_z \rangle \langle \uparrow_z | + |\downarrow_z \rangle \langle \downarrow_z |\right)$. Now it is much more plausible to define a wealth $w(|\psi_j \rangle)$ dependent on the state of the world.

For example, let us now consider an unfair "coin" represented by the density matrix $\rho = \frac{1}{3} \left(|\uparrow_z \rangle \langle \uparrow_z | + 2|\downarrow_z \rangle \langle \downarrow_z |\right)$. What is the probability of measuring this system in the state $|\uparrow_x \rangle$? That would be $\langle \uparrow_x | \rho | \uparrow_x \rangle = \frac{1}{2}$. Similarly, $\langle \downarrow_x | \rho | \downarrow_x \rangle = \frac{1}{2}$. It is interesting to note that equal probabilities are achieved for spin-up and spin-down in the $x$-direction (and $y$-direction as well) for this system; the difference is that now there are off-diagonal terms in the density matrix describing the degree of interference between the states of $S_x$ in the two populations of spins.

What can we do with this? Payoffs now need to be defined over every plausible noncommuting observable in the Hilbert space (because commuting observables yield the same state, and the payoff is really defined for the state). Thankfully this is fairly simple for spins, as the noncommuting observables in question are the components of $\vec{S}$.

Let us return to the previous unfair "coin". Classically (so it would be a coin), the result of the coin flip would be the end of the story. Let us suppose that the consumer had a risk-neutral utility $V(w) = w$. Let us also suppose that there was a game which payed off 20 if heads and 0 if tails and cost 10 to enter. The expected payoff, accounting for the cost of entering, would be $\mathbb{E}(w) = -\frac{10}{3}$, so the consumer would prefer to not play.
Classically that would be the whole story. Quantum mechanically, though, there is more to the story. If the owner of the game decided to measure $S_z$, then the result would be the same as the classical result. If the owner decided instead to measure $S_x$ or $S_y$, then $\mathbb{E}(w) = 0$ so the consumer would be indifferent between playing and not playing, which is certainly a different outcome from preferring not to play. In fact, if the consumer does not know for sure what the owner decides to measure, then probabilities could be assigned to the measurement choice itself, and these could then be used to find the expectation value of payoff or utility over all possible choices, where each of those choices will have an expected payoff or utility as well.

One thing to look further at is how to extend this to include continuous ensembles. The example in class was how a state of the world might be the outdoor temperature measured in some range. The quantum mechanical equivalent might be having a continuum of systems, each infinitesimal one having a position inside a given range of allowed positions; the only issue with this is that matter is not continuous, so I don't think it is possible to have a density matrix in the form of $\rho = \int |\psi(s) \rangle \langle \psi(s)| \, ds$ for some continuous index $s$. However, that can certainly be further investigated, and maybe I'll do that next time. The point is that states of the world in analyzing expected utility can easily be generalized to include quantum states through density matrices, and the question of which observable to measure in a noncommuting set brings out some interesting behavior not seen in classical states.

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