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Courtesy of abstrusegoose.com

About two years ago I bought a MacBook Air. I was worried about the lack of an optical disk reader, about the inaccessible battery and the presence of only one USB connection, but in the past two years I don’t remember ever needing the disk reader on the road (I have an external one at home), only a few times I wished for an extra USB port, and the battery has been holding up all right.

I have, however, encountered some completely unexpected problems. One is that the machine overheats very quickly if it does a computation-intensive task, and it has the “feature” that, if the temperature gets high, it shuts down one of the cores and makes the other go at about 40% speed. This means that it is not possible to connect it to a tv to watch movies from netflix or tv shows from hulu, because within half an hour it reaches the temperature that triggers the slowdown, at which point it skips so many frames that the movie looks like a slide show.

I also wish I could add more RAM. (The memory chips are soldered on the motherboard.)

Then last week I heard a cracking noise when opening it, and the screen would fall back instead of holding its position.

Despite the seemingly sturdy metal construction, the hinges had cracked:

Well, not a big deal, I thought, how expensive can replacement hinges be? Very expensive, a google search revealed.

The design of the computer is such that to repair the hinges they need to replace the screen. Not just the metal shell that covers the screen, but the LCD screen itself too, for a cost in the ballpark of \$800.

“Thankfully,” Apple will repair it for free even if my warranty has long expired.

The announcement of the free repair offer tells a story all by itself. First, that there should be an official policy for this problem shows how many people had this problem and how defective was the original design. (A google search also shows that.) Notice the compound design failures of having a break that (1) is so expensive to fix and (2) is so likely to occur. Second, the announcement offers a refund to those who paid for the repair in the past: indeed for a while people were having this break while their warranty was active and Apple would make them pay for the repair, claiming that the users were responsible for breaking the hinges, evidently because they used the computer in a way that it was not designed for, such by opening and closing it on occasion.

I just returned from a trip to Rome. While there, I was asked by my friends what I miss most of Rome. Of course what one misses the most is the city itself. Anybody who has walked around, and gotten lost into, the side streets around via del Corso or Trastevere, especially in the late afternoon, when everything is bathed in an odd yellowish light, knows what I am talking about. One thing I don’t miss is Roman traditional food. Roman cuisine is one of the worst of Italy’s and a lot of its delicacies gross me out. One famous dish for example, la pajata, has been (and probably still is) illegal since the emergence of mad cow disease, because it’s made from veal intestines, including digestive juices. The matter of its legality has preoccupied Rome’s mayor to no end, and he has threatened “eat-ins” of pajata as acts of civil disobedience.

Back to the things I miss, in random order:
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There are two families of approaches to proving circuit lower bounds: exploiting properties of functions computed by small circuits, and building hard functions by “brute force.” The first approach leads to “natural proofs” in the sense of Razborov and Rudich, which is a problem because natural proofs are unlikely to give lower bounds for circuit classes such as ${TC0}$ (constant-depth circuits with threshold gates), and maybe even ${ACC0}$ (constant-depth circuits with AND, OR, NOT, and MOD${_m}$ gates). The second approach creates proofs that “algebraize,” in the sense of Aaronson and Wigderson, and algebaizing proofs construct hard functions of very high uniform complexity; it is not even possible to use an algebraizing proof to show that the huge complexity class ${EXP^{NP}}$ contains problems of super-polynomial circuit complexity.

The ${NEXP \not\subseteq ACC0}$ circuit lower bound of Williams avoids both barriers, by exploiting (among other things) a property of ${ACC0}$ circuits (the existence of slightly faster-than-brute-force satisfiability algorithms) that is not a “natural” property, neither is an “algebraizing” property.

This post, written by a non-expert for non-experts (but experts are welcome to read it and to point out any mistakes), describes some of the context.