Comment by tossandthrow
4 days ago
Now calculate the probability that the professor at random selects the exact 10 problems that were solved correctly.
Your Eureka moment seems to be misinformed - I hope you can have it returned for another occasion.
It's just a random decaffeinated thought here this morning. Considering that it must be true that even a blind squirrel gets a nut once in a while it is also likely to be true that a professor at random can select the exact 10 problems that were solved correctly.
There's a difference between something with a probability of being true and another thing that is proven to be true. There are no doubts remaining after the proof whereas the probability always leaves wiggle room even if that wiggle room is a pretty tight space.
We should be careful about using probable and possible interchangeable.
You are right - it is possible that is happens but not probable.
However, overly focusing on this really deprives you of a lot of great intellectual stimuli from randomized algorithms and, like here, a large chunk of cryptography.
>However, overly focusing on this really deprives you of a lot of great intellectual stimuli from randomized algorithms and, like here, a large chunk of cryptography.
I agree with your first points about using probable and possible carefully. I originally posted a bit of a tongue in cheek, carefully selected example, from the full text of the article since that example fit the point that I hoped to make in jest. It was my carefully selected random example.
I think the focus of the article is on demonstrating that a tool used in cryptography to verify truth was widely assumed to be infallible and it turns out that is unfortunately not true since it can be manipulated to identify false results as true. This tool uses probabilities as a tool to minimize compute times that would be enormous if one had to verify absolutes so it is an important tool. Now that it is demonstrated that it can be successfully attacked, the basis of the system of verification is vulnerable and in the case of Ethereum at least, monetary losses can result.