Ehud Friedgut: Murphy’s Law of Breastfeeding Twins


This post is authored by Ehud Friedgut. Congratulations to Keren, Ehud and Michal for the birth of Shiri and Hillel!

Murphy’s law of breastfeeding twins, like all of Murphy’s laws, is supported by strong empirical evidence.

The twins’ feeding rhythm depends on your approach. If you decide to try and synchronize them in order to minimize your hassle and maximize your rest periods then twin A’s hunger will be governed by sine(t) and twin B’s by cosine(t).

If you decide to respect their natural rhythm in hope of falling into a fixed predictable pattern then twin A will follow sine(t) and twin B sine(\phi\times t), where \phi, the golden ratio, is the number hardest to approximate by rationals

(Eran Nevo) The g-Conjecture I

This post is authored by Eran Nevo. (It is the first in a series of five posts.)


Peter McMullen

The g-conjecture

What are the possible face numbers of triangulations of spheres?

There is only one zero-dimensional sphere and it consists of 2 points.

The one-dimensional triangulations of spheres are simple cycles, having n vertices and n edges, where n\geq 3.

The 2-spheres with n vertices have 3n-6 edges and 2n-4 triangles, and n can be any integer \geq 4. This follows from Euler formula.

For higher-dimensional spheres the number of vertices doesn’t determine all the face numbers, and for spheres of dimension \geq 5 a characterization of the possible face numbers is only conjectured! This problem has interesting relations to other mathematical fields, as we shall see. Continue reading

Michal Linial: Vive La Technology

    Nebi Samuel
    It was a long night after crossing the Atlantic. I got to the airport and indeed the big signs of ‘Welcome’ and “TAAM SHEL BAIT” (taste of home) had a special appeal. It was 3:30 in the morning when I took the Taxi. The driver was very talkative and wanted to know where I am coming from, are the stories that he had heard on America true. Specifically he wanted to know if I went to the Twins to see the city from the tallest buildings etc, etc.
    I replied shortly: “Yes, New York is as everybody said”. For the Twins, I replied: “No, there is no elevator there anymore”… I tried to be polite but at the same time to keep our touristy discussion to a minimum.  The Taxi driver turned out to be quite sensitive to my poor situation and told me very proudly: “Please tell me where, and I will take you, I have a new GPS, just tell me the address and the GPS will show me the way”. Indeed, I shared with him the importance of the GPS technology and even told him that I may soon buy one for my own car. My address is Nave Sha’anan 18, I told him, and 2 minutes later, I was asleep, this time very confident that in 45 min I am at home and to my bed. The next thing I know is Continue reading

1:0 to Italy: Michal Linial

Coming back from Hinxton, the most exciting genome center in the world and the most boring place after 5pm… At 5:30, a shuttle bus takes all the ‘workers’ to the big city – to Cambridge. The shuttle bus dropped us in the middle of town and without noticing, I remained alone. I quickly looked around; actually, there was no one on the street… OK I decided, the evening is not lost yet, I will go to London…
I waited 5 minutes and a Taxi stopped next to me. To the train station” I said. My taxi driver started the ride and then slowed down, stopped for a minute next to an open bar looked extremely worried and after 2 minutes speeded up again. We moved another 100 meters and again, he slows down and stop for 2 minutes next to a TV screen in the next open bar. He looks bothered and mumbled to himself, I hate him, Continue reading

Michal Linial – An Ambassador in Singapore


After the wonderful “being a cosmonaut” taxi-story, I am happy to present you:

 An Ambassador in Singapore

A story by Michal Linial


It was a long trip, 4 days in Singapore. I visited the tallest artificial waterfall in the world, and went on a night safari with artificial moon light. Well, time to go back home to reality. Before leaving my hotel, I made sure that I had enough money for a taxi ride to the airport. Due to last minute extra taxes, I found myself with only 15 Singaporean Dollars (~ 10 $ US). In the hotel, they promised me that it is more than enough. I entered the Taxi and immediately mentioned that I have 15$.

In the next 30 minutes my taxi driver explained that he actually does not want these 15$ at all. At the matter of fact, he is honored to take me to the airport as a treat of the Singaporean people to their distinguished guests. He said: ”I want your memories from Singapore to be enjoyable so you will tell everyone to visit us, and so you come back as well”. I was impressed. He continued: “my real satisfaction is to be the ambassador of my country”. He even went into some psychological arguments: “Can you remember the last time you were in Paris, can you tell me who took you to the airport?” I admitted that I did not remember, and then he continued: “Can you remember who took you to the airport from Jerusalem only 5 days ago ?” I had to admit that I did not remember any of this…and then he made his last point ”You will always remember me and you will want to come again to Singapore just because you met people like me”. Indeed, Continue reading

Cosmonaut: Michal Linial


Ladies and gentelmen, I am very happy to present to you:

Being a Cosmonaut

A story by Michal Linial

I am back from the airport… not in the best mood for a long discussion but quite open to hear refreshing political statements. 50 minutes taxi ride that is all what it takes… This time, the communication took its own turns… I start with my regular question: “What is new this week”. This time, my Russian Taxi driver ignored my question and asked back: “How many planets are there?” I told him that to the best of my knowledge there are 9 planets that orbit around the sun. Really, he shouted: “my wife tells me there are 8 and she tells me she is a cosmonaut” and he continues, she knows nothing! I said that there might be some debate, so 8 is a good number and probably I got confused. My Taxi driver got really mad now: “You are not a cosmonaut and you know better”.
Two minutes later, he asks me again “how old is the earth”. This time I was a bit less decisive and told my taxi driver that I am not sure, but the accepted number is 4-5 billion years. To make sure this time there will be no conflicts with his marriage, I immediately added, the universe is much older, also, many people believe that the earth is much younger. My taxi driver now is very excited and answers me without hesitation: “You see, I can not even ask my wife this question, she says she is a cosmonaut, but I am sure that if I ask her, she will not know”… Continue reading

Amir Ban on Deep Junior

Kasparov and Junior

Ladies and Gentelmen: Amir Ban (right, in the picture above) the guest blogger, was an Israeli Olympiad math champion in the early 70s, with Shay Bushinsky he wrote Deep Junior, and he is also one of the inventors of the “disc on key”. This post is about computer chess. 

Let me introduce myself: I’m Amir Ban, and I wrote the computer chess program Junior, also known as Deep Junior. When Gil invited me to guest-blog for him on the subject of computer chess, I was honored and pleased, but what can I write to introduce the subject to the uninitiated? Well, as luck has it, I participated last week in a unique event in Barcelona, Spain: a man with machine vs. machine match! The “man” was veteran grandmaster and Spanish champion Miguel Illescas. The “machine” he assisted himself by was my own Junior 10 (a commercially available product) on his Toshiba notebook. On the other side of the board was my latest Deep Junior 11, due to be released later this summer, running on an ordinary core-duo Dell desktop.

Susan Polgar, a former women’s world chess champion, and the eldest of the three Hungarian-Jewish Polgar sisters, describes the event on her popular blog. The comments to the blog entry show some difference of opinion:

Comment 1: “That’s not fair to the computer at all.”

Comment 2: “Big deal, Junior 10 vs. Junior 11 with a grandmaster moving the mouse….”

Visualization of Deep Junior Bxh2 sacrifice in the 5th game, New York, 2003.
Hmm… We need some perspective here. For that, let us take a few quick flashbacks, starting ca. 60 years ago with the pioneering efforts of Alan Turing, and especially Claude Shannon, who in 1950 wrote “Programming a Computer For Playing Chess“. In the article, Shannon lays out the foundations of computer chess, still practiced to this day: Given the current position where the computer must play a move, it will generate the tree of all hypothetical continuations: All moves playable at the position, then all possible replies to each of these moves, then all possible replies to the replies, and so on. Theoretically this process may continue indefinitely until a terminal position is reached, i.e. a checkmate, or a draw by the rules of chess. Unfortunately (or rather, fortunately) this possibility is merely theoretical, as the typical number of legal moves per position is around 40, and a chess game may last a hundred or so moves, the exponential explosion of possibilities forces a limit to the practical depth of the moves tree.

The Shannon trophy

Shannon proposed stopping the tree generation at some practical depth, and attaching an evaluation to the position at the leaf.

Continue reading