and that

These are neat facts that I picked up from reading Borwein & Borwein’s paper in the recent American Math Monthly. What other functions have that property?

Next week I am going to the International Congress of Mathematicians, where the Fields Medal will be awarded.  They still haven’t announced the winners, perhaps saving it for the conference.  It seems amazing to say this, but Deolalikar’s quiet announcement may have upstaged the Fields medal. The Fields medals have been upstaged before: by Perlman, who refused to show up despite proving the Poincare conjecture, and Wiles, who was stiffed by the arcane rules that the winner be under 40.

By the way if you write “P”, then “&”, “#”, followed by “8800 NP” without the quotes, you get the title of Deolalikar’s paper in HTML.

Update (14 August): Deolalikar has posted a summary of his proof on his HPL homepage.   He shows the essence of the proof is that k-SAT for k>9 grows exponentially, and thus there is no polynomial time algorithm.  K-SAT is the problem of checking whether a boolean expression ( X1X2(~X3)+X2(~X1)X3+…) with at most K literals per clause.

When I looked up P=NP on Google’s image search, I found this

On Homer’s right is P=NP.  On his left is Euler’s result, which when written

is the most beautiful formula ever.

Arguably, Apple’s best idea with iTunes is not building a store, but allowing people to buy by the song. Each song cost $0.99, which is just the right price–small enough that you won’t regret an impulse buy, but large enough to make you want to listen to a preview before you bought.

Imagine if  iTunes only let you buy by the album — around $9.99/album.  You would be a lot less tempted.  Why not just buy the CD at the store? That way you could have a permanent copy, with cover art, possibly a lyric sheet, and also be able to play it in the car.  No, buying by the song made a huge difference and in my opinion accounted for iTunes’s success (and Apple’s). And it allowed electronic music to be sold for the same amount as a physical version, despite the obviously huge profit margin to Apple from not having a physical store selling physical media.

Now comes the iPad.  It’s purpose is to sell books and magazines. I don’t see how the book sales will work.  You can’t sell books by the chapter. You have to sell the whole book, and if that is sold for the same amount as a physical copy, to follow the music model–around $10 for a general book and $100 for a textbook, who would buy it?  Books already cost too much.

I’m waiting for college students to start ripping their very-expensive textbooks. They can use any of the designs shown here

http://www.diybookscanner.org/

The cost of a diy scanner is less than the cost of an iPad. It’s essentially 2 cameras, and a light source, connect to a pc with some software. If you have the patience to scan a text book, about 2-4 hours, then you can carry around the pdf coveniently on a laptop or in a book reader like the iPad.

I can’t wait for someone to build a page-turning robot arm addition.

Yahoo bought Associated Content recently.   This looks to be a news source with an online model of sourcing freelance writers, but it also seems in the business of selling ads — so lots of stories about celebrities, weight loss, hair gain, and sex.

NPR in the USA is a great reporter, but does not have an investigative arm.  The BBC is an even better reporter of world events, and frequently has some of the best interviews.

The New York Times is one of few remaining papers that actually has writing by people qualified to discuss issues, like Paul Krugman.   I like Gail Collins and David Brooks as well.

Singapore has the Straits Times, which is owned by the government. It’s job is to put a good word out for Singapore and the government.  Letters to the editor frequently offer compliments to a public official for polite service.

A friend sent me online news sources in Singapore that aim to discuss issues. One of the better ones is the Online Citizen .   I started reading this only today but found the level of writing and discourse is high.  An interesting theme in one article is whether Singapore’s immigration policy (aiming for an increase in population from 5m to 6.5m) will lead to a loss of identity and culture.  That’s what everybody fears world wide, but I can say that in California, with nearly 1/3 of the population born outside of the usa, would on the whole be much less fun, and much worse off economically, without its immigrants.

It used to be the fashion to buy components rather than design your own.  Computer companies like HP have long done this: intel-samsung-nvidia design and (intel - samsung) fabricate the chips, taiwanese and chinese companies assemble them into motherboards and printers and pcs. And MSFT makes the software.  HP spun off Agilent which spun off Avago, which actually designs chips.  Nobody wanted to design chips.

Apple took the build over the buy : they designed their own OS and have excellent product design.  They also used to rely on the chip companies for their components, but they bought P.A. Semi to design their own processor, used in the iPad, and rumour has it, the next iPhone.

Video compression used to be another component that people bought rather than built.  You could buy the rights to use MPEG-4 or H.264 through MPEG-LA, and deploy that technology on your encoder.  Google is taking another tack: it bought On2 , and plans to open up the source of that companies’ video compression technology to enable the “WebM” format.  Regardless of how good WebM is compared to H.264, if it is even 70% as good, I doubt anyone will notice.  One simply has to shrink the resolution to achieve the same number of bits.  3G bandwidth is more than enough for streaming video and flash storage is cheap.

I’ll wait a few years for the management fashion to swing back to buy rather than build.

Chrome is apparently the only browser that does DNS prefetching. The reason, according to Chromium blog, is that it speeds up DNS resolution (by a few hundred ms) by using the time otherwise wasted while you are typing in a URL to fetch the IP address.  I imagine that it works by having Chrome run a separate thread to fetch IP addresses of whatever is related to your recent visit, so that the time spent typing (which is a relatively slow activity) is concurrently spent on fetching IP addresses.

For some reason, this multi-threaded activity fails — possibly there is a livelock.  The browser hangs, with the unhelpful message “resolving host…”.

I found that turning off prefetching got rid of the hanging browser and made life much better.

(1 + 0.49 + 0.49)/3  x 100% = 66%

However, party S has only won 1 seat, despite having 2/3 of the total vote, whereas R has two seats with only 1/3 of the vote.

In a PR scheme, some seats are set aside without a district and are allocated to a party according to the party’s share of the vote, so that a fairer allocation occurs. For example, suppose we set aside 2 non-district seats (call them D and E).  Then, in the scenario above, party R gets seats A and B, party S gets C, and in addition, the additional non-district seats D and E.  So now, party S has 3/5 seats in parliament, and becomes the majority, which matches its share of the vote.

I’m a big fan of PR: it’s power to the people, and one cannot reasonably oppose fair distribution of seats according to votes.

What if Singapore had PR? In the 2006 election, the ruling party of Singapore, the People’s Action Party (PAP), got 66.595% of the vote, but secured 82 of the 84 seats because of the FPP voting rule.   If PR were in place in Singapore, the PAP would have received 56 seats, in theory.  That is exactly 2/3 of the Parliament.  This is important, because in Singapore more than 2/3 of the Parliament must approve any Constitutional change. Hence, with PR, the PAP wouldn’t have enough votes for constitutional tinkering.

On 27 April of this year, Singapore’s constitution was changed in Parliament to increase the number of  non-district representatives, from 15 to 18.  These additional representatives are guaranteed to come from a party other than the ruling party.  However, 9 of those non-district representatives (is there a better name?) are nominated by parliament.  Gee, who thought of that? The other 9 are the best-performing losers in the district elections.   What is the role of these non-district representatives?   Here is what they cannot vote on

• amendment of the constitution
• public funds,
• vote of no confidence in the government
• removing the president from office

Nice list, isn’t it?

That was then.  Today, Apple makes products which do not open or extend in any easy way. The iPhone is a great example.  It doesn’t have a flash memory card that you can save data on (like a pdf file).   As everyone knows, you can’t change the battery.   There are no screws to let you take it apart easily.  Even inserting a sim card is done through a cumbersome slot that requires you to fold open a paper clip and stick one end through a tiny hole.

Then there is Flash.  Apple does not support Flash because, in theory,  Flash lets you create an App on a web page.  That means people can create apps without needing to sell the App on the iTunes store (and paying Apple 30% of the revenue).

If you take a photo with the iPhone 3G, the photo is stored in JPEG format which doesn’t contain EXIF information (exposure time, f#).   It is the only phone or camera that I know of which is so secretive.

It’s well known that the iPad doesn’t support Flash either.  There are predictions that Flash will die out because of the advent of HTML5. If it turns out to be possible to write web-hosted Apps using HTML5 ,don’t look to Apple to support it.  Control is everything to the most secretive company.

Genting is an entertainment complex, with gambling for adults and arcade games + amusement park rides for families.  One kid asked to go on a ride with me, because he was all by himself. I hope that’s not because his parents were off gambling.  Apparently, anyone is allowed to gamble at Genting, except for Malaysian Muslims.  In contrast Malaysian Indians, Chinese are allowed to gamble, and even Muslims from other countries are allowed in the casinos.

I didn’t gamble but I did enjoy the cool air of the mountains. The fog rolled in while we were there and covered the park.   It was neat to see the carousel riders in the mist.

Genting, with Kuala Lumpur in the distance

The hotel where we stayed apparently had more than 6,000 rooms.  It was huge.

Here are more pictures of the amusement park and hotel

Caterpillar train in the fog, Genting

Our hotel in the fog

after the fog rolled in.

It’s also the smallest car I’ve driven. Even in the parking lots around NTU, it’s about the dinkiest car around.  Here is a photo.

The car is supposed to get 50mpg easily. I’ll report on the results I get this month.

1 Feb 2010: First tank of gas, mileage is 13.6 km/liter, or ~32 mpg.  Not as much as I would have hoped.

Why don’t we have city cars in America?