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Last weekend I went to see the Swiss national circus Knie here in Lausanne.

In their amazing show they also had a juggler, juggling with tennis rackets. While I was watching his performance I was thinking: “Man, he is sooo lucky that there is gravity. He should try that in outer space!”.

That’s my current age in days.

It occurred to me today while running that I had missed the chance to celebrate my 10,000th, well, I would say “diaversary“. However, the term “diaversary” seems to refer to your “birthday” as a diabetic, though I’m not sure if this is the day of the diagnosis or what exactly it marks.

Anyways, I’ll probably celebrate the 12345th day of my life. Of course, this nice pattern of increasing digits is rather arbitrary, as it depends on the decimal system. If you write the same number in binary you get 11000000111001. So it’s not so much a property of the number itself as of its representation. In the meantime, I might also celebrate my 10809th day, as this is a lucky number. [Yes, there’s a mathematical definition for a number to be a “lucky number”.] The property of being a lucky number is, just as the property of being a prime number, independent of the representation. So this is as good an excuse as any to celebrate.

For the nerds: The Goldbach’s Conjecture also seems to hold for pairs of lucky numbers, which are always odd.

Ok, this actually happened quite a while ago, but I never wrote it down (… and I certainly don’t want to forget this incident).

About  a year ago I went to Potsdam for a small scientific workshop. On one evening I also went out to dance salsa. On my way back to my accommodation (… obviously I was staying with a host from the hospitalityclub …) at about 1am I had to wait for a tram for about 10 minutes. While I was waiting, a young guy in his late teens walked up to me and asked me: “Got a paper?” (O-ton: “Haste mal ‘nen Paper?”)

Now, as most of you will probably know, the word “paper” in my daily languages refers to a scientific publication. As I happened to have a couple of “papers” in my bag, I was even more puzzled by this question and couldn’t quite figure out, why this random youngster would be interested in scientific literature at 1am in the morning.

A couple of seconds (and a very confused look from my vis-à-vis) later I eventually replied: “No, sorry.”

It took me what felt like an hour to realize that he had asked me for rolling paper for cigarettes.

I recently came across this collaborative poetry project. It is a simple website where the whole world can share one magnetic poetry kit. I really like this mix: 20% collaboration, 30% nerdness, and 50% creative poetry.

Now creating short “poems”, as beautiful and worthwhile as it may be, is unlikely to solve any of the world’s problems. But could a similar approach be harvest to do something useful?

When it comes to sharing computer resources, there are projects such as SETI@home, which combine the computational powers of people worldwide to create a supercomputer to work on a common goal. The basic idea is: your computer downloads small data chunks. Runs some analysis on the data, and sends the results back to the server (after a few hours/days) to get some more data to work on.

Can you think of any intellectual problems, which

(i) could not be easily solved by a computer

(ii) require human “creativity” or at least human thinking

(iii) could be broken up into small chunks, which can be solved by an intelligent person in anything between a few minutes and a few hours/days

(iv) where the “solution” to each chunk is somehow easily verifiable (ideally by a machine).

Then one could create  such as joint project for “real” problems:

Each evening, before you go home, you could “download” a small sub-problem to work on over the next few hours or whenever you have time. Once finished you then upload a “solution” and download the next problem. [These could, e.g., be a simple but non-trivial Lemma as part of a big proof.]
Wikipedia (… this is the first time I looked at the Wikipedia article about Wikipedia. Is there a Brockhaus entry in the Brockhaus?) is probably the best example for what a joint intellectual project can do. But this project would be different in nature. Ideally, you would not need to be online to think about your small chunk and the final output would be the solution to a real problem.

Just as SETI@home (and similar projects) helps to avoid that any CPU cycles “go to waste”, this project would in a sense help to avoid that brain capacities “go to waste”.

Google has an interface in Klingon. Check it out here.

jlSuDrup!

[By the fact that this fact was new to me, you can tell that I’m only a pseudo-nerd.]

Tit-for-tat was beaten in the iterated prisoner’s dilemma tournament in 2005 and I only found about this now!

THE example of game theory in a nutshell:

“Two suspects, A and B, are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal: if one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must make the choice of whether to betray the other or to remain silent. However, neither prisoner knows for sure what choice the other prisoner will make. So this dilemma poses the question: How should the prisoners act?”

The dilemma:

1. If you’re one of the prisoner’s it is always “best” (in the sense of a short prison sentence) for you to betray the other person, regardless of how this person behaves.

2. This holds by symmetry for the other person too.

3. If both people act “rationally” they will  both go to jail for 5 years. Quite a lot.

4. If they both act “nicely” (and count on the other’s co-operation) they’ll be free after 6 months. Not a lot.

5. So you’ll think: Ah, so they co-operate! – Not so fast! If person A knows/assumes that person B will be nice, he has no reason to be nice himself. Unless he’s afraid of  person’s B big brother or some other form of retaliation. For a “single round” of “this game” you simply cannot “rationally” justify co-operative behavior.

But this is different, if we “play repeatedly”! Then I need your good will for the future rounds.
Suppose it’s not about serving time in prison, but about getting points, the more points the better.

If both confess, both get only 1 point.  If both co-operate (= shut up), both get 3 points. If one confesses/defects and the other co-operates/shuts up, then the person who confesses will get 5 points, the person who remained silent will get 0 points.

So now we play this game repeatedly. Then I suddenly need your co-operation in several rounds. If I betray you now, I might get 5 points, but then you’ll probably betray me in the next rounds, and I won’t be able to get more than 1 point anymore.

Funny thing: This reasoning only works, if the number of rounds is unknown!

If we know in advance that we’ll play, say, 10 rounds, then I know that in the last round you have no reason to co-operate with me. Hence, I already have no reason to be nice to you in the 9th round, as in the next round you can do what you want anyways (as there is “no tomorrow”). So neither me nor you will co-operate in the 9th round either. But then, why co-operate in the 8th round? Etc…

So this game is only fun to play, if you don’t know the number of rounds in advance, and this is exactly what was done in this tournament (where computer programs were the players/prisoners).

Ok, if you’ve followed so far, just stay with me a bit longer and you’ll get the punchline.

In this tournament, where any super complicated way of choosing to defect or to co-operate could participate, the winning strategy (i.e., the one which accumulated the most points accumulated in a number of “matches”) was a very simple one: tit-for-tat!

You start by co-operating, i.e., by playing nicely. Then you do whatever the other player did in the last move.

This is the Cold War kind of strategy: I start by not dropping by my nukes. If you didn’t drop your nukes last week, then I won’t drop my nukes this week.

Tit-for-tat … unbeaten for 20 years … fascinating … at least for a computer geek!  🙂

Finally, it was beaten 3 years ago!

But, it took a very cleverly choreographed group of 60 players to beat it. These players had some designated “slaves” and “masters”. The slaves would always sacrifice themselves when playing against one of the masters, but the slaves would be always defecting when playing against outsiders, whereas the masters would play a tit-for-tat in those cases. The really clever thing: The rules of the game usually do not leave any room for “communication”, i.e., I can’t simply tell you “Hey, I’m also in your group!”. So the program always sacrificed the first 10 moves to “communicate” through its decisions about defection or co-operation (think ‘handshake‘ if you’re a nerd).

Pretty clever, but ultimately it still seems that as an individual strategy the tit-for-tat performs best.

I just took a simple multiple choice mathematics test, with one question taken from each school year in Germany. I can proudly say that I managed to answer all 13 of them correctly! So, at least in mathematics, I still deserve my Abitur. 🙂

If you know some elementary German, have a look at the test here.

Admittedly, I “cheated” for some of the questions as it was, for example, easier/quicker to verify each of the three given integer solutions for a system of linear equations, than to solve the system of equations by hand. In fact, I even simplified the check further by using modular arithmetic (base 10). In other words, I only checked the last digit. Let me know, if there are even quicker ways to “solve” such multiple choice questions.

Solid, liquid, gas.

Ok, in fact there are many more: plasmas, quark-gluon plasma, Rydberg matter, Bose-Einstein condensates and fermionic condensates, quantum spin Hall state, degenerate matter, strange matter, superfluids and supersolids, and possibly string-net liquids. (This list was taken from the Wikipedia article on state of matter.) But why are there any discrete states at all? Why is there not just one continuous level of “blurriness”? Maybe with one or two other dimensions to describe the state.

I couldn’t find an explanation on the Wikipedia page but I assume this is simple stuff (as long as one doesn’t continue to ask “why” too often). With atoms I’m fairly ok with the discrete level of states/orbits for the electrons. “That’s just the way it is.” Or at least the explanation is on a low enough level for me to swallow it and not to ask any further.

But the state of matter is an inter-atom/inter-molecular thing (it doesn’t make sense, I think, to say that an individual atom or molecule is in solid state) and it should somehow be possible to derive an explanation form the description of individual molecules (just as one can make statements about which molecules will form by only looking at the individual  atoms). Where does this additional discreteness of our existence come from? Can anybody point me in the right direction? Maybe this is standard A-level chemistry/physics stuff.

Why is all matter limited to a discrete set of states?

I don’t really care about car racing. But the DARPA recently held a rather different kind of “car race” which every nerd simply has to love: The DARPA Urban Challenge

“Vehicles competing in the Urban Challenge will have to think like human drivers and continually make split-second decisions to avoid moving vehicles, including robotic vehicles without drivers, and operate safely on the course. The urban setting adds considerable complexity to the challenge faced by the robotic vehicles, and replicates the environments where many of today’s military missions are conducted.”

Can a robot car obey traffic rules? Can a robot car parallel park?

Watch the official video (27MB) or try your luck on youtube to find out.

Needless to say that the DARPA probably cares less about traffic rules than about building fully automated killing machines.

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