Good questions to think about

[prane]

I have a very boring summer job to earn some money and often find myself passing the time with thoughts of science (mainly physics) and maths.

I would really appreciated it if you shared with me some cool questions/topics to think about to help me escape the boredom of putting shopping trolleys away!

 

[cosmik debris]

Figure out if the complexity class P=NP.

 

[GarageDweller]

How GR can be unified with QFT.

Also, how to get windows to stop updating on its own.

 

[NascentOxygen]

how to get windows to stop updating on its own.

Linux will fix that problem.

 

[davenn]

Linux will fix that problem.

hahaha ... some one just had to say it!

well done

Dave

 

[DrewD]

The things you might enjoy thinking about really depend on what you know.

Do you know $$\Sigma_{n=1}^{\infty}x^n$$
and for what values of $x$ this equals a number?

Perhaps you could think about every aspect of the trolley and how it was designed. Is it the way it is because
a) there are physical laws that prevent it from working properly if it were designed otherwise
b) there are many other ways to design it, but the way it is designed is aesthetic and efficient
c) there are monetary reasons for not making in a way that it would work better
d) there is a lazy stupid engineer somewhere that has already forgotten that he/she helped design this piece of junk

think about all levels from the geometry to the materials and what machines would have been used to create it.

I always think angular momentum is interesting. Reread your texts and think about angular a gyroscope. Angular momentum is so important throughout much of physics.

If you send a binary code to a friend to convey a simple statement, what is the best way to assign strings of numbers to the letters/words that you want to send to your friend? What should you agree on before hand?

Since I don't know if these are above your knowledge level or below your knowledge level, I won't keep going. I would recommend picking up a few books with some of your hard earned cash, reading them at night, and thinking about them in the day. Popsci can be good for this if you haven't read them all already. You can also find cheap used textbooks if you are beyond the point of enjoying popsci.

Or you could calculate exactly how much money you make while going to the bathroom in a given week. Just some mental arithmetic, but it can be nice especially if you don't like your boss.

 

[prane]

The things you might enjoy thinking about really depend on what you know.

Do you know $$\Sigma_{n=1}^{\infty}x^n$$
and for what values of $x$ this equals a number?

Perhaps you could think about every aspect of the trolley and how it was designed. Is it the way it is because
a) there are physical laws that prevent it from working properly if it were designed otherwise
b) there are many other ways to design it, but the way it is designed is aesthetic and efficient
c) there are monetary reasons for not making in a way that it would work better
d) there is a lazy stupid engineer somewhere that has already forgotten that he/she helped design this piece of junk

think about all levels from the geometry to the materials and what machines would have been used to create it.

I always think angular momentum is interesting. Reread your texts and think about angular a gyroscope. Angular momentum is so important throughout much of physics.

If you send a binary code to a friend to convey a simple statement, what is the best way to assign strings of numbers to the letters/words that you want to send to your friend? What should you agree on before hand?

Since I don't know if these are above your knowledge level or below your knowledge level, I won't keep going. I would recommend picking up a few books with some of your hard earned cash, reading them at night, and thinking about them in the day. Popsci can be good for this if you haven't read them all already. You can also find cheap used textbooks if you are beyond the point of enjoying popsci.

Or you could calculate exactly how much money you make while going to the bathroom in a given week. Just some mental arithmetic, but it can be nice especially if you don't like your boss.

Some good suggestions here but thought about most of them already :p.

For the first example, We only have convergence for all |x|<1 and not equal to 0 right?

 

[DrewD]

...then start on cosmik debris's question