As humans, we are often too quick to say that something is impossible and move on. Often it pays to double-check - what exactly have we shown to be impossible and does this really matter? Sometimes we'll find it is actually possible, sometimes it'll just give us another idea, but in both these cases it is useful.
Example 1: Can a computer work without power?
Suppose you've been teleported into the past, but you would to be able to solve a calculation. You have no way of generating electricity. Just because an electronic computer like the one you buy at the store needs power, it doesn't mean that you can't build a mechanical computer that doesn't need power. (clarifying computer)
Suppose you're making a computer. Surely, it can't be expected to do anything when the power is off? But what about if it is e-ink, then it can display something static. (clarifying work)
Suppose you want to give children laptop with educational programs, but the town has no sources of electricity. You invent the OLPC laptops, which are powered using handcranks. (clarifying without power)
In each of these cases, it would have been very easy to think, "Computers need power" there is nothing that I can do, when this wasn't the case. Not that we ended up clarifying each phrase - "computer", "work", "without power"
The barber says that they shave every man in the town, but no man shaves themselves.
If you haven't heard this before, this brainteaser might be hard or it might be obvious. Regardless, we can make it even easer by clarifying each phrase.
What does "in the town?" mean? Maybe they mean everyone who lives in the town and doesn't include people who work in the town.
What if the barber is not a man? What if they are a women?
The second is the proper solution, but it comes out very easily once we start clarifying exactly what is impossible?
Example 3: Being attractive
Suppose a person wants to be attractive. Suppose they find out that being attractive requires them to be tall and have lots of muscles because they live in Shallow Land. Unfortunately, they are short and can't gain muscles no matter how much they train. Perhaps, they even become depressed because of this.
On the other hand, what is meant by "attractive"? What do they actually want? Perhaps they don't mean "attractive to most people", but "attractive to a reasonable subset of people"? So perhaps they will never have most people seeing them as attractive, but they could become attractive within the intelligentsia sub-culture. Or perhaps they only need to be attractive enough to find someone to marry? The initial no turned out to be less important than it seemed.
Take-aways
One of the key lessons here is that language is slippery. It's very easy think think, "That's impossible, let's move on", without realising that the thing that is impossible is actually rather limited.
Even when it is actually impossible, we can generate ideas by trying to discover what is the closest that we can get to achieving something that is impossible.
The main technique to accomplish this, it to attempt clarify each word or phrase. If you do this, then ideas drop out pretty quickly.
As humans, we are often too quick to say that something is impossible and move on. Often it pays to double-check - what exactly have we shown to be impossible and does this really matter? Sometimes we'll find it is actually possible, sometimes it'll just give us another idea, but in both these cases it is useful.
Example 1: Can a computer work without power?
In each of these cases, it would have been very easy to think, "Computers need power" there is nothing that I can do, when this wasn't the case. Not that we ended up clarifying each phrase - "computer", "work", "without power"
Example 2: Barber Paradox (wiki)
The barber says that they shave every man in the town, but no man shaves themselves.
If you haven't heard this before, this brainteaser might be hard or it might be obvious. Regardless, we can make it even easer by clarifying each phrase.
The second is the proper solution, but it comes out very easily once we start clarifying exactly what is impossible?
Example 3: Being attractive
Suppose a person wants to be attractive. Suppose they find out that being attractive requires them to be tall and have lots of muscles because they live in Shallow Land. Unfortunately, they are short and can't gain muscles no matter how much they train. Perhaps, they even become depressed because of this.
On the other hand, what is meant by "attractive"? What do they actually want? Perhaps they don't mean "attractive to most people", but "attractive to a reasonable subset of people"? So perhaps they will never have most people seeing them as attractive, but they could become attractive within the intelligentsia sub-culture. Or perhaps they only need to be attractive enough to find someone to marry? The initial no turned out to be less important than it seemed.
Take-aways
One of the key lessons here is that language is slippery. It's very easy think think, "That's impossible, let's move on", without realising that the thing that is impossible is actually rather limited.
Even when it is actually impossible, we can generate ideas by trying to discover what is the closest that we can get to achieving something that is impossible.
The main technique to accomplish this, it to attempt clarify each word or phrase. If you do this, then ideas drop out pretty quickly.