> 1) What does it mean that entangled particles are supercorrelated? How can S(A|B) = 2 or -1?
The density matrix does not have the same properties of a joint probability distribution, so quantum entropy doesn't really have the same properties of classical entropy. 
> 2) The formula for Von Neumann entropy is S = -Tr(p log(p)), where p is the density matrix. How do you take a log of a matrix?
The log of a matrix is defined as the inverse of the matrix exponential. The matrix exponential can be defined as the usual power series, only using matrices rather than scalars.
What one usually does is: diagonalize the matrix (if possible), take the log of the eigenvalues and rotate again. Obviously taking the log of a matrix is a little trickier than the exponential because if you have negative or complex-valued eigenvalues you have to be a bit more careful.
Good answers. Just a small comment: quantum entropy is a generalization of classical entropy. In particular, if A and B are classically correlated, then S(A|B) has all the properties of a classical entropy (Shannon's, in this case), for instance, it is non-negative.
Ha, I was thinking of the same thing. Who knows, maybe he's built for this kind of thing. On that note : if he can get a good night's sleep after all that caffeine, then I envy this man's constitution, which can absorb so much caffeine and still not reel from it! Poor me has to strictly follow a no-caffeine after 6 p.m. rule if I have to get any sleep. Actually, come to think of it, the only time I can handle coffee gracefully is right after I wake up from sleep.
I find it's really hard to make a homemade espresso that comes close to the one you get from a café around here. But then again maybe I should invest 10k on a new machine (and then 20k to renovate my kitchen to fit it in).
I got mine second hand (insolvency auction) for $900 for a machine that would have cost $6,000 when it was new a couple of years ago, and later I spent $400 on a grinder that goes for $1200 new. Both in good working order, apart from having to replace the hopper on the grinder ($70 for a piece of plastic was annoying).
Totally worth it though. The grinder (and coffee beans - buy them no later than a week after roast) are the most important part really.
> It's pretty difficult to find anything outside on par with the quality I can get at home (most of the time..)
It really depends on where you are. I find that espresso in the gourmet cafés in large American cities I tried is mostly on par or slightly worse than the average espresso in Rome. The grains and the roast can be pretty good, but it's often brewed slightly long for my taste.
Espresso here is so dense it's almost solid and that's the thing I can't reproduce at home.
Are crowdfunding platform going to be the home shopping channel of this decade? There seems to be a lot of resemblance with the miracle products with dubious claims and ripoffs that are more expensive than the original.
It is different, but it's not any less an injustice. One could even argue that it's worse in some sense.
Let me play the devil's advocate: an homosexual couple cannot conceive a child, so by giving then them the chance to adopt your somehow extending their natural rights. On the other hand restricting one's freedom of movement because one was born in the wrong country seems completely arbitrary.
Don't get me wrong, I fully support the struggle of homosexuals for equal rights, but why it's considered acceptable to maintain that non-citizens have less rights than citizens escapes me. It should be exposed as xenophobic behavior, exactly like campaigning against homosexual marriage is homophobic.
I highly doubt most of that stuff will be publicly accessible. A friend told she had a very hard time finding the documents she needed for her thesis at the Vatical Library. She had the definite impression, after a lengthy process to get clearance, that the inventory was kept patchy on purpose to make it hard for external visitors to find stuff in the allotted time.
“All manuscipts digitised through this operation will be released on the Vatican Apostolic Library's website as high-definition data. As a result, numerous researchers in the fields of academia and in various fields of knowledge will be able to interpret the valuable manuscripts, to which access had long been restricted, in their original form”, declared the president of the NTT Data Corporation.
The interview process is short and straightforward, or at least it was in my case, but the indexing system is a nightmare and a patchwork of centuries of amateur and professional librarians cobbling together catalogs. Some of the collections can only be referenced using catalogs that are 250+ years old--literally. I don't mean copies or modern printings of the catalogs. I mean literally some dude wrote on the pages in front of you 250 years ago and that is the tool that you are supposed to use to find your sources. Yes, very low quality facsimiles are tucked away in a corner of the reading room, but you need to figure out which catalog they're in to find them...
One definitely wonders at some point whether the whole thing is organized as a conspiracy to confuse new Ph.D. students!
I defer to your friend's expertise on the subject, but really, the Church isn't trying to hide anything. This was not the case when the ASV opened to the public in the late nineteenth century when in fact the Vatican's hope was that researchers would read their documents and write nice things about the church. These days, however, the ASV is one of Europe's main archives, curated by respected professionals. There is no hidden agenda.
A more likely reason why your friend had such a hard time was Napoleon, who made a policy of transferring all the grand archives of the countries he conquered back to Paris. An enormous number of documents were lost during the transfer and the eventual repatriation, somewhere around one third. Records relating to Galileo's trial were lost, for example. Of course, the most likely reason that your friend and I had difficulty is just the incredibly user-unfriendly systems of cataloging that the ASV uses.
At the risk of sounding like an apologist for the Vatican, I should also point out that the fact that these archives are open at all is remarkable. These aren't a national archive, for instance, where the state maintains records as a service for its citizens and to keep the nation's heritage alive. The ASV is quite simply the dumping ground for the Vatican's bureaucracy over the past 1700 or so years. They don't owe this to anyone.
It would be like if Microsoft pooled all documents generated by HR, marketing, product development, engineering, legal, and its other divisions, physically dumped them in various containers over the centuries, and one day in the year 3749 A.D. announced that the public could rifle through the papers if they wanted to. The immediate impetus would be to demonstrate that Office 3750 was not in fact part of an anti-competitive plot to secure a monopoly on productivity software sold in Alpha Centauri and Venus. But by 3800 A.D., that original purpose would have been long forgotten and researchers, regardless of which office suite they use, would be able to mine the archives for anything that anyone working for Microsoft ever said, did, or observed during the work day, so long as those thoughts were captured on some format that eventually made its way to paper.
...to make the analogy more complete, let's also assume that most of the other major institutions and their archives have been wiped out by this time. What ends up happening, then, is that researchers in 3749 A.D. dig through MS' archives for glimmers of things like what people ate during the day in 2014 or what sort of music they listened to.
> How are we going to attract and recruit the best engineers unless we've got a reputation for the very best and most foolish April Fools trickery?
I would actually discourage anyone from taking a job from any company that takes April Fools too seriously. Having to put in extra hours to get the April Fools out in time is the only thing that's more soul-crushing than the stupid corporate joke itself.
Spending some time to actually raise the mood of your clients is a no-go place for you? I assume your preference is to work for a no-emotion company 100% dedicated to the product, and a casual chit-chat is a strong NO policy.
The question is whether a joke is funny and made you smile of course.
> Not the first place that would come to mind for precision manufacturing, but there you have it.
Why not? Aren't Swiss watchmakers in the Alps as well?
And regarding sibling poster saying they have production mainly in China: I remember reading they've actually moved some of the production to Italy after acquiring firms that were making their frames in China. If I find a source in English I'll post it.
Indeed, I feel like I'm one of the few people that uses my phone almost entirely as a tool. I don't use any social network for entertainment (only for messaging), and though I do use it browse the web, my use there is largely negligible.
However, I do get a HUGE amount of use out of my phone as a tool. I handle email, keep notes, use the camera for notes, manage files using Dropbox, and listen to music/podcasts (which help me be productive). I don't feel like phones are a bad thing.