Several Big Numbers to Sort

1. number of pretty human faces
2. the smallest number not expressible with 1000 Python  lines
3. number of possible stable molecules
4. the decimal place of the number Pi, where the Java coded superintelligence begins
5. the largest well defined natural number on the Internet today (April 30, 2017, 12:00 GMT)
6. the inverse of the probability, that the Zeus is in charge
7. the inverse of the probability, that the Moon is actually a medium size pizza in the sky
8. the inverse of the probability, that the fall of Rome was staged and that the current Pope is a Cezar, deceiving all but those Roman families who still run the world
9. the inverse of the probability, that you will be reincarnated, remembering all, before 2100
10. the number of all the people that could have been born, if the history went differently enough for them
11.  the number of possible worlds better than this
12. the inverse of the probability, that I run the simulation you are currently in

You may sort just a pair, find two (maybe zero/infinite) equals, find the minimal or the maximal number, the average.

But you may also sort the whole list.

A Moral Problem

You have several hundred school kids, who choose their elective subjects, two or three of them (4 hours per week at the most in total), for the entire next school year.

It is possible for the school to have 25 of those subjects, chosen among 36 possibilities. So they ask kids, what they wish to learn. Each student makes his or hers top 5 list.

The most wanted was German language, the least demanded was Chinese language. 30 students wanted German language as their number one choice and 10 students wanted Chinese language as their number one choice.

Fortunately, exactly 25 subjects were even mentioned by students. The only problem is, that the group of 30 students is too big and should be split into two smaller, for the law and safety reasons. But then, one other group has to be canceled. Those 10 who wanted Chinese should accept some secondary choice like music, sports, experimental chemistry and so on. There will be no Chinese course next year.

Or, 2 of those 30 who wanted German language should accept some less desired choice like painting or philosophy and then there will be room for the Chinese language course.

This is a frequent real life dilemma I saw many times in the last 10 years. In reality it’s more complicated than that, but essentially the same.

It is easy to say – well kids, there won’t be no Chinese language course next year, due to the lack of interest and our limitations. But it is harder to say, there will be no German language just for you 2, despite the fact that other 28 will have it.

What is the right thing to do?

 

 

 

Logic Problem

This statement has the letter “T” at the beginning; the next two letters are “h” and “i”; which are followed by “s s”; … ; the first letter is then repeated inside double quotes; …

Question. Not only that this statement is true and has infinite length, but also uniquely and completely describes every English statement possible. Those which are of a finite or countably infinite length. Is that possible?

Physics Question

Fast receding galaxies, is their metabolism  apparently slowed down due to some relativistic effect, or not?

For example, supernovae (type I, for example) should be dimmer, right?

And any other type of stars or whatever object do shine at a slower rate.

Don’t they?

 

Another Intermezzo Intermezzo Problem

The first one was solved by Oscar Cunningham and the point of the solution is that every probable black hole lasts for at least a million years longer, if you add just one hydrogen atom into it. Of course, a supermassive black hole acquires even much longer additional time with every hydrogen atom acquisition, or shall we say — a merger with a single hydrogen atom.

It is reasonable to assume, that our domestic SMBH’s lifespan is prolonged by 10^60+ years per second, due the regular infall. Assuming also, that there will be no Big Rip or something equally unpleasant for black holes in the future.

While we still don’t know the definite answer to the Intermezzo problem, here is another inter-intermezzo.

Are there non synthesizable molecules, which would be stable if they somehow managed to pop up into existence by magic or by some weird quantum fluctuation? (Non-synthesizable-repeatedly from chemistry/physics/mathematics/logic reasons.)