7. Today's serving shall involve three stories of the extraordinary Hungarian mathematician John von Neumann (1903-1957)
The following problem can be solved either the easy way or the hard way. Two trains 200 miles apart are moving toward each other; each one is going at a speed of 50 miles per hour. A fly starting on the front of one of them flies back and forth between them at a rate of 75 miles per hour. It does this until the trains collide and crush the fly to death. What is the total distance the fly has flown? The fly actually hits each train an infinite number of times before it gets crushed, and one could solve the problem the hard way with pencil and paper by summing an infinite series of distances.
The easy way is as follows: Since the trains are 200 miles apart and each train is going 50 miles an hour, it takes 2 hours for the trains to collide. Therefore the fly was flying for two hours. Since the fly was flying at a rate of 75 miles per hour, the fly must have flown 150 miles. That's all there is to it.
When this problem was posed to John von Neumann, he immediately replied, "150 miles."
"It is very strange," said the poser, "but nearly everyone tries to sum the infinite series." "What do you mean, strange?" asked Von Neumann. "That's how I did it!"
8.
Student: "Er, excuse me, Professor von Neumann, could you please help me with a calculus problem?"
John: "Okay, sonny, if it's real quick -- I'm a busy man."
Student: "I'm having trouble with this integral.
John: "Let's have a look." (after a brief pause) "Alright, sonny, the answer's two-pi over 5."
Student: "I know that, sir, the answer's in the back -- I'm having trouble deriving it, though."
John: "Okay, let me see it again." (another pause) "The answer's two-pi over 5."
Student (frustrated): "Uh, sir, I _know_ the answer, I just don't see how to derive it."
John: "Whaddya want, sonny, I worked the problem in two different ways!"
9. Von Neumann (like our own Srinivasa Ramanujan) supposedly had the habit of simply writing answers to homework assignments on the board (the method of solution being, of course, obvious) when he was asked how to solve problems. One time one of his students tried to get more helpful information by asking if there was another way to solve the problem. Von Neumann looked blank for a moment, thought, and then answered, "Yes".
The following problem can be solved either the easy way or the hard way. Two trains 200 miles apart are moving toward each other; each one is going at a speed of 50 miles per hour. A fly starting on the front of one of them flies back and forth between them at a rate of 75 miles per hour. It does this until the trains collide and crush the fly to death. What is the total distance the fly has flown? The fly actually hits each train an infinite number of times before it gets crushed, and one could solve the problem the hard way with pencil and paper by summing an infinite series of distances.
The easy way is as follows: Since the trains are 200 miles apart and each train is going 50 miles an hour, it takes 2 hours for the trains to collide. Therefore the fly was flying for two hours. Since the fly was flying at a rate of 75 miles per hour, the fly must have flown 150 miles. That's all there is to it.
When this problem was posed to John von Neumann, he immediately replied, "150 miles."
"It is very strange," said the poser, "but nearly everyone tries to sum the infinite series." "What do you mean, strange?" asked Von Neumann. "That's how I did it!"
8.
Student: "Er, excuse me, Professor von Neumann, could you please help me with a calculus problem?"
John: "Okay, sonny, if it's real quick -- I'm a busy man."
Student: "I'm having trouble with this integral.
John: "Let's have a look." (after a brief pause) "Alright, sonny, the answer's two-pi over 5."
Student: "I know that, sir, the answer's in the back -- I'm having trouble deriving it, though."
John: "Okay, let me see it again." (another pause) "The answer's two-pi over 5."
Student (frustrated): "Uh, sir, I _know_ the answer, I just don't see how to derive it."
John: "Whaddya want, sonny, I worked the problem in two different ways!"
9. Von Neumann (like our own Srinivasa Ramanujan) supposedly had the habit of simply writing answers to homework assignments on the board (the method of solution being, of course, obvious) when he was asked how to solve problems. One time one of his students tried to get more helpful information by asking if there was another way to solve the problem. Von Neumann looked blank for a moment, thought, and then answered, "Yes".
5 comments:
Entertaining :D
" Yes " ...:D Priceless.
thanks for stopping by guys :)
When Claude Shannon derived in his seminal paper on information theory the concept of information entropy, he was wondering what name should he give to it. The form of the expression was exactly like the entropy defined in classical statistical mechanics (\sum P Log P)
von Neumann suggested that he should call it entropy. He thought that there was so much confusion about the nature of entropy in physics that if an electrical engineer starts calling something entropy, it would make it worse. And it did!
Okay not so funny :-(
PS: von Neumann along with Eugene Wigner were both chemical engineers because at that time in Hungary, chemical engineering was the only challenging program :-)
@purshya: That story was funny. What is more funny is that the two of us are chemical engineers too :P
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