It would have been even more frustrating had the protagonist not also been guessing the teacher’s password. It seemed that the protagonist just had a better memory of what more authoritative teachers had said.
The protagonist was closer to being able to derive π himself, but that played no part in his argument.
There’s no evidence that the protagonist didn’t just have a better memory of what more authoritative teachers had said.
The protagonist knew that pi is defined as the ratio of a circle’s circumference and diameter, and the numbers that people have memorized came from calculating that ratio.
The protagonist knew that pi is irrational, that irrational means it cannot be expressed as a ratio of integers, and that 7 and 22 are integers, and that therefore pi cannot be exactly expressed as 22⁄7.
The protagonist was willing to entertain the theory that 22⁄7 is a good enough approximation of pi to 5 digits, but updated when he saw that the result came out wrong.
The protagonist knew that pi is defined as the ratio of a circle’s circumference and diameter, and the numbers that people have memorized came from calculating that ratio.
The protagonist knew that pi is irrational, that irrational means it cannot be expressed as a ratio of integers, and that 7 and 22 are integers, and that therefore pi cannot be exactly expressed as 22⁄7.
These are important pieces of knowledge, and they are why I said that they protagonist was closer to being able to derive π himself.
The protagonist was willing to entertain the theory that 22⁄7 is a good enough approximation of pi to 5 digits, but updated when he saw that the result came out wrong.
The result only came out wrong relative to his own memorized teacher-password. Except for his memory of what the first five digits of π really were, he gave no argument that they weren’t the same as the first five digits of 22⁄7.
I try to avoid criticizing people when they are right. If they genuinely deserve criticism, I will not need to wait long for an occasion where they are wrong.
I try to avoid criticizing people when they are right. If they genuinely deserve criticism, I will not need to wait long for an occasion where they are wrong.
I did not criticize the protagonist. He acted entirely appropriately in his situation. Trying to derive digits of π (by using Archimedes’s method, say) would not have been an effective way to convince his teammates under those circumstances. In some cases, such as a timed exam, going with an accurately-memorized teacher-password is the best thing to do. [ETA: Furthermore, his and our frustration at his teammates was justified.]
But the fact remains that the story was one of conflicting teacher-passwords, not of deep knowledge vs. a teacher-password. Although the protagonist possessed deeper knowledge, and although he might have been able to reconstruct Archimedes’s method, he did not in fact use his deeper knowledge in the argument to make 3.1415 more probable than the first five digits of 22⁄7.
Again, I’m not saying that he should have had to do that. But it would have made for a better anti-teacher-password story.
I see what you mean. I think the confusion we’ve had on this thread is over the loaded term “teacher’s password”—yes, the question only asked for the password, but it would be less misleading to say that both the narrator and the schoolteachers had memorized the results, but the narrator did a better job of comprehending the reference material.
It would have been even more frustrating had the protagonist not also been guessing the teacher’s password. It seemed that the protagonist just had a better memory of what more authoritative teachers had said.
The protagonist was closer to being able to derive π himself, but that played no part in his argument.
The protagonist knew that pi is defined as the ratio of a circle’s circumference and diameter, and the numbers that people have memorized came from calculating that ratio.
The protagonist knew that pi is irrational, that irrational means it cannot be expressed as a ratio of integers, and that 7 and 22 are integers, and that therefore pi cannot be exactly expressed as 22⁄7.
The protagonist was willing to entertain the theory that 22⁄7 is a good enough approximation of pi to 5 digits, but updated when he saw that the result came out wrong.
These are important pieces of knowledge, and they are why I said that they protagonist was closer to being able to derive π himself.
The result only came out wrong relative to his own memorized teacher-password. Except for his memory of what the first five digits of π really were, he gave no argument that they weren’t the same as the first five digits of 22⁄7.
Y’know, there’s something this blogger I read once wrote that seems kinda applicable here:
I did not criticize the protagonist. He acted entirely appropriately in his situation. Trying to derive digits of π (by using Archimedes’s method, say) would not have been an effective way to convince his teammates under those circumstances. In some cases, such as a timed exam, going with an accurately-memorized teacher-password is the best thing to do. [ETA: Furthermore, his and our frustration at his teammates was justified.]
But the fact remains that the story was one of conflicting teacher-passwords, not of deep knowledge vs. a teacher-password. Although the protagonist possessed deeper knowledge, and although he might have been able to reconstruct Archimedes’s method, he did not in fact use his deeper knowledge in the argument to make 3.1415 more probable than the first five digits of 22⁄7.
Again, I’m not saying that he should have had to do that. But it would have made for a better anti-teacher-password story.
I see what you mean. I think the confusion we’ve had on this thread is over the loaded term “teacher’s password”—yes, the question only asked for the password, but it would be less misleading to say that both the narrator and the schoolteachers had memorized the results, but the narrator did a better job of comprehending the reference material.