What’s the title of this post?

When crossing the road with my father and my children, he told me that I shouldn’t just look around for cars, but also tell my children to look around for cars. I told him that he is to blame that I’m not doing that because when I was a child, he only told me to look around for cars, so I’ve learned only to do that. Later I’ve realized that I should tell my children the following sentence: ‘Look around for cars, and tell your children twice ‘Look around for cars, and tell your children twice”.’

Premove chess theory

(I just remembered my wonderful blog, the prefect place to cross off things from my todo list without actually doing them!)

Most online chess sites allow one to make a premove, which means that we select our next move without knowing what the opponent moves, and the computer automatically executes the move (if it doesn’t contradict the rules). It can be quite useful when one is running out of time. However, I don’t think it’s theory has been studied yet much. For example,

• Is it possible to checkmate a solo king with a king and a queen?

Here selecting a premove that cannot be executed should count as losing. But we can assume that our opponent takes a long time to move each time, so this question is not about speed, but about an appropriate premove in each step.

One can potentially allow mating sequences that are successful with 100% probability after some time, but with 0% probability black can escape eternally. This is similar to the ZPP class in complexity theory. For example, we can move with our queen left or right, and if the black king moved in the opposite direction, we win, but if it moved in the same direction, we stay in the same situation.

• Are there any situations when we cannot mate surely but we can with 100% probability?

What Is the Kolmogorov Complexity of This Book?

I’m happy to announce that I came up with a brilliant title for my upcoming book – now only the inside part of it is left to do…

Radon numbers grow linearly

Feel free to leave comments here about my arXiv preprint with the above title.

Exponential lower bound for Berge-Ramsey problems

Feel free to leave comments here about my arXiv preprint with the above title.

Anyone to fine

One problem with fining, for example, cars parking like assholes, is that it requires a lot of staff walking around the city. Calling the police is a lot of time and the car might leave by then. Giving the right for anyone to impose a fine wouldn’t work, as we can only accept evidence from reliable sources. So here is my proposal to cut this Gordian-knot.

Anyone can place a fine notice on any car they wish. These look exactly the same as the ones that are placed by officials. If the driver pays the fine, then the story is over, the municipality keeps the money. If the driver doesn’t pay, then if the finer was not an official, they got away. (They might do this hoping this was the case, or if they feel unjustly fined.) If the driver doesn’t pay and the finer was an official, then they get a second fine after two weeks, which is the double of the first. (And if they think it was unjust, they can still appeal etc, do the standard procedure.)

Software to play against with real cards

I prefer to play with real cards than on the computer, but sometimes there aren’t enough people for a game. I wonder why no one has yet made a software to which you can show its hand (without you seeing them, like turning the cards towards the devices camera), and then the AI would tell you each time what it does, like play the 2nd card from top of the hand.

A chance of capital punishment instead of jail sentence

Suppose that instead of jail sentences, the verdicts for serious crimes would be certain probabilities of capital punishment. For example, suppose that for a 30-year-old man, whose life expectancy is roughly 80 years, instead of 1 year in prison, he would get executed with 1/(80-30)=2% probability. With the remaining 98%, he could go free without any punishment.

Putting aside the moral issues with this proposal, for whom it would be better than the jail sentence? For the state, the costs would be obviously much lower. (Assuming that the convict let loose wouldn’t go on committing serious crimes with high probability.) But would it be more or less deterrent than jail sentence? If given the choice, which option would convicted criminals prefer? Other thoughts/social implications?

In fact, optionally the dice can be cast ahead the whole trial – this way in 98% of the cases, it can be skipped! But this would probably influence the judge/jury too much, if they know that a death sentence is in the air… Or would this model anyhow influence them?

Tributum Alma Mater

Now that so many people inside the EU end up working in another country, shouldn’t a part of their tax go back to the country where they were educated? But seriously, why not?

What would you do alone when you’re about to die?

Suppose some scenario when you know for sure that you’ll die in a couple of hours and you would need to spend them on your own. What would you do? Write some note that you can leave behind? Make a last attempt at your favorite conjecture? Or just watch a movie? Or post a last one on your blog? In fact, the question has two versions, depending whether people would later know what you did or whether no one would ever find out…