Here's what I told my parents over dinner one day:
You have a problem that needs to be solved and a way of solving it that takes a certain amount of time. I the problem grows, how much longer will it take to solve with that same method? If the problem is twice as big, will it take twice as long?
For example, I need to move a steak from one plate to another. My method is to use a knife and fork to cut the steak into bite sized pieces and move each piece to the other plate. If I have two steaks, I can expect this method to take twice as long. What if I have 10 steaks? It might take a bit of work to make room to properly cut a steak. At 20 steaks, I probably just don't have room on the plate anymore and it takes much longer than 20 times the time to move those steaks than it did to move 1 steak.
Now let's say my method is to just dump the contents of the first plate onto the second plate. If I have two steaks this takes about as long to do. What if I have 10 steaks, or 20? It starts getting clumsy and the time it takes to move them using this new method gets longer at a predictable rate. At 200 steaks I probably can't just dump one plate onto the other, I can't even lift the plate!
The question then is, up to how many steaks is the second method better than the first? Is it always better as the number of steaks goes up? Is there a better steak moving method? What if we change the container from plates to something else?
You have a problem that needs to be solved and a way of solving it that takes a certain amount of time. I the problem grows, how much longer will it take to solve with that same method? If the problem is twice as big, will it take twice as long?
For example, I need to move a steak from one plate to another. My method is to use a knife and fork to cut the steak into bite sized pieces and move each piece to the other plate. If I have two steaks, I can expect this method to take twice as long. What if I have 10 steaks? It might take a bit of work to make room to properly cut a steak. At 20 steaks, I probably just don't have room on the plate anymore and it takes much longer than 20 times the time to move those steaks than it did to move 1 steak.
Now let's say my method is to just dump the contents of the first plate onto the second plate. If I have two steaks this takes about as long to do. What if I have 10 steaks, or 20? It starts getting clumsy and the time it takes to move them using this new method gets longer at a predictable rate. At 200 steaks I probably can't just dump one plate onto the other, I can't even lift the plate!
The question then is, up to how many steaks is the second method better than the first? Is it always better as the number of steaks goes up? Is there a better steak moving method? What if we change the container from plates to something else?