Hi all,
when a solution to a problem appears, it is easy to verify that solution solves the problem, or you would have another problem and not a solution, no?
Consider the below problem
Pick a coin choose a side and flip it as freely as you want to live.
After you can guess the side the coin ends up facing you right all the time and regardless of the time and space you live, I have a question for you.
Why didn't you come here now to tell me about it stop writing before I finish this question here?
The above is a problem whose solution is easy to verify for correctness, but the problem isn't easy to solve, no?
Because if any problem was easy to solve, someone could predict the future, but next doesn't happen next in imagination really, next happens next in reality.
In case you are wondering why next doesn't happen next in your imagination, if you had a problem with me writing the above, why didn't you come earlier to tell me about it?
What, you thought I might be afraid to face you prophet?
Nah, this isn't what seems to be happening prophet, something else is happening here...
Another way to explain...
1.You are asking, if the solution to a problem is easy to check for
correctness, must the problem be easy to solve?
2. When a solution for the problem appears it is easy to check that
this solution solves the problem, or else you would have
another problem, and not really a solution.
3. A problem needs to start a path in time and space which ends
with a solution for this problem, in order for the problem to be
solved in time and space, or else all paths in time and space
with a beginning, a middle, and an end wouldn’t solve this
problem.
4. if it is easy to solve…
5. it is easy to check that the solutions solve the problem, or you’d
have more problems,
6. or you didn’t find this path… … so pick a coin, choose a side, and flip it as freely as you want
to live.
7. After you can guess the side the coin ends up facing you right all
the time, I have a question for you.
8. Why didn’t you come here to tell me about it now?
https://en.wikipedia.org/wiki/P_versus_NP_problem
If the solution to a problem is easy to check for correctness, must the problem be easy to solve? (google it)
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butimfeeling2022
- Posts: 93
- Joined: Fri Feb 18, 2022 10:57 pm
Re: If the solution to a problem is easy to check for correctness, must the problem be easy to solve? (google it)
I'm sorry, butimfeeling2022, your question does not pass the Turing test. Can you summarise it in more conventional terminology?
Re: If the solution to a problem is easy to check for correctness, must the problem be easy to solve? (google it)
I would say that the late-19th C problem of the "Eternal Recurrence", made famous by Nietsche (though not his own idea), is an example of a question which was not easy to solve, but for which the solution was (retrospectively) easy to check for correctness. In fact, this may be the normal situation for most scientific solutions, almost by definition.
In Nietsche's day, scientists and cosmologists believed that the universe was a simple Euclidean infinity. It had always existed, always would exist, and was infinite in every direction. It fell to a brilliant French mathematical physicist, Henri Poincare, to point out the difficult implications of this. Poincare was one of the few scientists of the time who was familiar with statistics (itself, then, a new science), and, in particular, the laws of statistical probability. Poincare proved - with irrefutable arguments - that if the universe was really infinite as contemporary science supposed, then there must exist infinitely many perfect copies of the planet Earth. There would also exist infinitely many copies where, instead of God, Satan would be worshipped as the supreme deity (this was not, I should point out, part of Poincare's original argument).
This was a huge cat among the scientific, philosophical, and religious pigeons. If Poincare was correct - and his arguments were irrefutable - then all of religious and moral science was reduced to absurdity; hence the appeal of the concept to Nietsche.
The problem of the Eternal Recurrence was only solved a generation later, with Einstein's theories on relativity, and the further elaboration of non-Euclidean geometry.
This is not the only example in scientific philosophy, of course. The Watson-Crick model and the Darwinian theory of evolution were easy enough to check after the event.
In Nietsche's day, scientists and cosmologists believed that the universe was a simple Euclidean infinity. It had always existed, always would exist, and was infinite in every direction. It fell to a brilliant French mathematical physicist, Henri Poincare, to point out the difficult implications of this. Poincare was one of the few scientists of the time who was familiar with statistics (itself, then, a new science), and, in particular, the laws of statistical probability. Poincare proved - with irrefutable arguments - that if the universe was really infinite as contemporary science supposed, then there must exist infinitely many perfect copies of the planet Earth. There would also exist infinitely many copies where, instead of God, Satan would be worshipped as the supreme deity (this was not, I should point out, part of Poincare's original argument).
This was a huge cat among the scientific, philosophical, and religious pigeons. If Poincare was correct - and his arguments were irrefutable - then all of religious and moral science was reduced to absurdity; hence the appeal of the concept to Nietsche.
The problem of the Eternal Recurrence was only solved a generation later, with Einstein's theories on relativity, and the further elaboration of non-Euclidean geometry.
This is not the only example in scientific philosophy, of course. The Watson-Crick model and the Darwinian theory of evolution were easy enough to check after the event.