mathematics

Alpha-Primes Problem

Which minimal length English sentence describes the set of all  primes smaller than 100?

You can use numerals as well.

 

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physics

And Another Physics Problem

The one I talked about before, but it is very obscure, even unknown on the whole World Wide Web.

We have two equal stars, A and B. Then we have a planet called X in the orbit around A, and a planet called Y around the star B.

Everything else equal, except for the rotation speed of both planets. Planet X rotates 20% faster than planet Y. The question is, which planet has a higher average surface temperature.

Edit: See discussion:

http://lesswrong.com/r/discussion/lw/p1m/open_thread_may_22_may_28_2017/dsis

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Chesslike Problem

Long ago, I invented a problem which solution looks like this:

configuration

The problem was to place a complete set of white chess pieces on the chessboard such that the number of bonds between them is maximal. Here you see that the king protects 8 neighboring pieces and the pawn in the top line covers no piece. The number of all protections is 53 and it can’t be done any better. (You may notice a pawn in the first line and those bishops are of the same color, but that’s fine.)

If you now add 40 more queens and rearrange all those 56 pieces, then there will be at most 338 bonds in total. We call that number B – the maximal bonding number for the set F. For all the white pieces it’s 53, for 2 knights only it’s 2, and so on.

We have a set F with bonding number B1. And a proper subset F’ with the bonding number B2. B1 is equal to B2. Which set is that?

In other words, for which set you can remove one or more pieces and the maximal binding number remains the same as it was initially.

There is a trivial solution of any single piece and the empty set, but as always, we want a nontrivial solution.

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Some Ideas I’ve Noticed

Some, at least, are worth mentioning. How good they really are is debatable. But I generally like most of those, described below.

  1. Fashion, says Jim, is upstream of everything. One picks his ideas according to what is high status and that’s that. In the Soviet Union being a Christian wasn’t high status, but in the today Russia, it is. It is not a question of how you deliberate and ponder about the Holy Trinity or any other Orthodox Christianity/politics/science stuff, because you can’t do much pondering anyway. You just use your status perceiving as a proxy when idea shopping. Jim says, now we have a transition into more “ancient regime” or aristocratic, Trumpetian fashion, which is easy to spot and difficult to imitate. A situation as it was centuries ago.
  2. Jordan Peterson says, that no matter if you are a male lobster or a male human, you are born into this serotonin driven male hierarchy as the most important environmental determinant. Girls have their own status piramide, a bit different than boys, but basically, we are all in this. He also says that we got our exceptional eyesight thanks to snakes and fruits. We had to see what was good fruit and where a snake was crawling. Eve’s legend is very much about this.
  3. A friend of a friend of mine has an idea where instead of fracking, you put some special bacteria deep down into the Earth’s crust to eat all the methane there. In the process, those bacteria would produce electricity which you pick up by a cable and bring to the surface. Fracking version II, or “electricity fracking”.
  4. It’s a good time to be dead now, and alive much later when the Universe will be much colder. Then, the amount of computing available will be many orders of magnitude greater. Every second then will count for a trillion or so current ages of the Universe now. Save for the future, they say.
  5. Use Neural Networks for everything! They say that if you don’t know how to solve any solvable problem by using NN’s now, don’t worry, those networks will soon be able to do it. Or eventually. Who thought that they could learn to play Super Mario and Go that well.
  6. Imagine, that agrumes like lemons, oranges, and more than 20 others suddenly died out. What an annoying disaster that would be! A luck of the same magnitude (but with the opposite sign, of course) – would be rubitia. An unknown family of fruits, as broad as agrumes, obtainable with genetic tampering with bananas or apples or something. We don’t know how to do it yet, but one day we will. The eatable universe is also huge.
  7. Immutable databases, where no record is ever deleted or even edited, only new are added. Information is too valuable to erase. Erase nothing, from now on! The same goes for RAM. Never overwrite a bit! When you absolutely must do that, save it first to the immutable database. And blockchain everything, too!
  8.  The human history is a cycle. Hard times create strong men. Strong men create good times. Good times create weak men. Weak men create hard times.
  9. There is a problem with some nova star far, far away, but in this Galaxy. When it had exploded back in 2003, or there about, it was just a nova. A decade later, its remains travel apparently (much) faster than light. They say that everything is under control because this is only an illusion. I can understand the alleged effect reasonably well, but I am only 99% sure that it is really the case.
  10. A few days ago, I caught a folk song on the radio. “A poor sinful soul has died and gone to loudly knock on Heaven’s door and nobody heard her knocking. So she went to very cautiously knock on Hell’s door also. Satan heard her immediately.”

 

 

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Problem With Perspective

Imagine, that you are an intelligent bird with a 360 degrees, panoramic view, flying over a plane equipped with orthogonal x and y axis, clearly visible and – what a coincidence – intersecting just 10 meters beneath you.

I argue, that due to the well-known phenomenon of the geometrical perspective, you see in a distance the line which goes North, parallel to the line which goes West. In fact, every direction seems parallel to all other three directions.

Is that right, and why it’s right? How could this be?

 

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