physics

# My Bet

This “EM reactionless drive” is not going to work. It doesn’t work.

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mathematics

# Geometry Problem

Say that you have an empty transparent cube. Then you put a reflective sphere inside – the biggest possible one. And then the next biggest possible reflective sphere. Or 8 of them, or any number of them. And so on.

You may consider a supertasking to do it, or just say that this is your transparent cube, packed with distinct reflective spheres of different sizes. There is no room for another sphere inside, no matter how small it would be.

Now, you beam an ideal ray toward one of the cube’s outer square’s midpoint. It will just reflect from the biggest sphere. The angle of incidence may even vary, doesn’t matter.

Now you beam a ray in the direction of one of the cubes main diagonals – from outside toward the center. Will it:

1. bounce back immediately after reaching the corner
2. bounce back after some finite time
3. exit at the opposite corner after some finite time
4. exit somewhere else after some finite time
5. never come out again
6. This is an illegal or ill defined question

What say you?

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mathematics

# An Even More Difficult Problem

The same as the last one for the number Pi, except that only the first X digits are allowed to be mapped into instructions and then executed. So, an infinite loop and a finite size algorithm obtained from the first few hundred (more or less)  instructions. The decimal dot is merely a comment.

3.1415 … is perhaps INC A; A+=1/A; NOP; A+=1/A; NOP …

1 is bolded and the corresponding function A+=1/A is bolded to explain this somewhat more.

The initial A value is of course 0.

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mathematics

# Another Math Problem

This one isn’t as easy as the previous.

Take the number Pi in any base you want. Assign its every digit with some function/operation, such that so transformed Pi is now a Pi generating algorithm.

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mathematics

# Quine Number Problem

I have promised, long ago, that I will devise some math problems. Here is one.

Say that we have a number 8 written in binary (base 2) as 1000.

Now, we have two basic operations: INC and SHL.

INC increases a number by 1, SHL shifts a number left by 1 binary digit. It’s the same as the multiplication by 2.

We will code SHL as 0 and INC as 1. So the sequence 1000 means:

INC A; SHL A; SHL A; SHL A

At the beginning A=0, and it is A=8 (or 1000 in binary) at the end. We want to begin with zero and end up with whatever number is calculated.

The number 8 reproduces itself (in base 2) using those two operations, therefore it’s called a Quine number. 3 (or 11 in binary, or INC A; INC A) – makes 2 out of initial zero. So it’s not a Quine, for 2 not equal 3.

The problem: Which two, if any at all, operations makes any number a Quine number in base 2?

You may take ternary numeral system (base 3) and three basic instructions, such that every number is a Quine. Or base N, with N basic (not necessary different) operations/instructions as well.

(For N=1, for the unary numeral system, the solution is rather trivial. 7 decimal or 0000000 in base 1 – and INC coded as 0 – 7 gives you 7. X gives you X for every natural.)

Is there any nontrivial solution; above this base 1 with the INC operation?

Smaller values of base are better!

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Uncategorized

1. Actually, I won a bet that he would win on November 8th.
3. He will make America great again. He really means that (and is capable of doing so – or maybe just psychologically incapable of merely  squandering all those years in Oval office).
4. At the end of his reign, technology will explode for other reasons.
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# My Outlandish Belief

You have probably seen metronomes and how they automatically synchronize after some time. Putting them on a moving platform helps them synchronize even faster.

Say, that there are just two metronomes and that one is virtual – a real time physical simulation of a metronome – and the other is a real thing. At least, in some special circumstances, they will be synchronized as well.

No magic required.

Now say, that we have a certain Turing complete physical process inside an ordinary computer, which is also known as “a running program” or “an active executable” or just “a process”. Can a computer nearby catch it and run it as another instance? If this program was a yawn transmitted among several people early in the morning on a commuting train?

It happens all the time, no magic required. Not even a cable between two boxes.

But what if there were only one computer and one big rock? If the computer were running SOMETHING here on Earth, and a rock were on the Moon. Can this SOMETHING induce such a change inside that rock, that another instance of SOMETHING will be running there, on the Moon?

I believe that’s possible and that this will be the way that the whole Galaxy will be colonized and transformed one day. No magic required.

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