Can all supposed difficult problems be broken down to simple ones?

[Hacker Jack]

I am wondering if you take any problem you consider difficult or complex can it be broken down to be understood in simple parts and successfully understood as a whole. Is there some stuff you consider difficult and there is just no getting around it.

Is it the nature of the brain to focus on one thing at a time to understand something or is there so much more stuff going on in the background that our brain does that we don't understand?

 

[Klystron]

From your username I presume an interest in computer science. Nicklaus Wirth uses the interesting term stepwise refinement: refining or decomposing a complex solution into simpler, though not necessarily discrete, solvable parts. Though sometimes confused with top-down and bottom-up approaches, the steps approach the problem space from any convenient direction.

Stepwise refinement applies to problems with solutions. Deciding whether stated problems can be solved probably requires complexity theory. Consider also the time and resources required to solve.

 

[HAYAO]

It depends on what you call "simple", but in science, we often use approximations that simplify the problem. Of course, every time you use an approximation, there are some information that is lost or things that cannot be taken into account. Nonetheless, by using approximations, you can often understand the general idea.

 

[berkeman]

I am wondering if you take any problem you consider difficult or complex can it be broken down to be understood in simple parts and successfully understood as a whole. Is there some stuff you consider difficult and there is just no getting around it.

Is it the nature of the brain to focus on one thing at a time to understand something or is there so much more stuff going on in the background that our brain does that we don't understand?

What's up with your avatar? Are you a pirate or into death or something? How can I take your technical questions seriously when your avatar represents bad things?

 

[StevieTNZ]

What's up with your avatar? Are you a pirate or into death or something? How can I take your technical questions seriously when your avatar represents bad things?

View attachment 275047

Just as bad as this avatar:

 

[mfb]

If you could break down everything into arbitrarily simple steps you could teach calculus to a dog. How? Step by step.

I'm not even sure if the steps are the limit. It could be the current state of a problem, too: Where are we in a proof, what do we know about the objects we are working with at the moment, what do we still need to do?
If you have read some longer mathematical proofs then you probably know the feeling where you can follow every step, but in the end you don't really understand what was done because you are still missing deeper insight in the proof.

 

[Evo]

Sorry, but we don't allow threads that ask "What if, and have no answer". Thread closed.