Existence Proof
An engineer, a physicist and a mathematician are staying in a hotel. The engineer wakes up and smells smoke. He goes out into the hallway and sees a fire, so he fills a trash can from his room with water and douses the fire. He goes back to bed. Later, the physicist wakes up and smells smoke. He opens his door and sees a fire in the hallway. He walks down the hall to a fire hose and after calculating the flame velocity, distance, water pressure, trajectory, etc. extinguishes the fire with the minimum amount of water and energy needed. Later, the mathematician wakes up and smells smoke. He goes to the hall, sees the fire and then the fire hose. He thinks for a moment and then exclaims, "Ah, a solution exists!" and then goes back to bed.
here's another, my favourite
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Reducing to Previously Solved Problems
There were two men trying to decide what to do for a living. They went to see a counselor, and he decided that they had good problem solving skills.
He tried a test to narrow the area of specialty. He put each man in a room with a stove, a bucket of water, and an empty pot on the stove. He said "Boil some water in the pot." Both men filled the pot with water from the bucket and turned on the burner to boil the water. Next, he put them into a room with a stove, a bucket of water, and a pot full of water on the stove. Again, he said "Boil the water in the pot." The first man immediately turned on the burner. The counselor told him to be an Engineer. The second man emptied the pot and proudly said that now the problem is reduced to the previously solved problem. The counselor told him to be a mathematician.
note how the engineer is always the builder - the one who always innovates or re-creates solutions from scratch. the engineer works hard!
the scientist is also concerned with practical solutions, but wants to spend minimal effort on applying it. the scientist scabs off an existing solution (fire extinguisher) and applies it to a good approximation.
the mathematician isnt concerned with specific circumstances - create the general solution and let others use it. innovating is just redundancy - u just need the axioms!
An engineer, a physicist and a mathematician are staying in a hotel. The engineer wakes up and smells smoke. He goes out into the hallway and sees a fire, so he fills a trash can from his room with water and douses the fire. He goes back to bed. Later, the physicist wakes up and smells smoke. He opens his door and sees a fire in the hallway. He walks down the hall to a fire hose and after calculating the flame velocity, distance, water pressure, trajectory, etc. extinguishes the fire with the minimum amount of water and energy needed. Later, the mathematician wakes up and smells smoke. He goes to the hall, sees the fire and then the fire hose. He thinks for a moment and then exclaims, "Ah, a solution exists!" and then goes back to bed.
here's another, my favourite
...Reducing to Previously Solved Problems
There were two men trying to decide what to do for a living. They went to see a counselor, and he decided that they had good problem solving skills.
He tried a test to narrow the area of specialty. He put each man in a room with a stove, a bucket of water, and an empty pot on the stove. He said "Boil some water in the pot." Both men filled the pot with water from the bucket and turned on the burner to boil the water. Next, he put them into a room with a stove, a bucket of water, and a pot full of water on the stove. Again, he said "Boil the water in the pot." The first man immediately turned on the burner. The counselor told him to be an Engineer. The second man emptied the pot and proudly said that now the problem is reduced to the previously solved problem. The counselor told him to be a mathematician.
note how the engineer is always the builder - the one who always innovates or re-creates solutions from scratch. the engineer works hard!
the scientist is also concerned with practical solutions, but wants to spend minimal effort on applying it. the scientist scabs
off an existing solution (fire extinguisher) and applies it to a good approximation.the mathematician isnt concerned with specific circumstances - create the general solution and let others use it. innovating is just redundancy - u just need the axioms!
