Skip to comments.Mathematicians Discovered a Computer Problem that No One Can Ever Solve
Posted on 01/12/2019 5:15:03 AM PST by BenLurkin
The trouble is, math is sort of broken. It's been broken since 1931, when the logician Kurt Gödel published his famous incompleteness theorems. They showed that in any mathematical system, there are certain questions that cannot be answered. They're not really difficult they're unknowable. Mathematicians learned that their ability to understand the universe was fundamentally limited. Gödel and another mathematician named Paul Cohen found an example: the continuum hypothesis.
The continuum hypothesis goes like this: Mathematicians already know that there are infinities of different sizes. For instance, there are infinitely many integers (numbers like 1, 2, 3, 4, 5 and so on); and there are infinitely many real numbers (which include numbers like 1, 2, 3 and so on, but they also include numbers like 1.8 and 5,222.7 and pi). But even though there are infinitely many integers and infinitely many real numbers, there are clearly more real numbers than there are integers. Which raises the question, are there any infinities larger than the set of integers but smaller than the set of real numbers? The continuum hypothesis says, yes, there are.
Gödel and Cohen showed that it's impossible to prove that the continuum hypothesis is right, but also it's impossible to prove that it's wrong. "Is the continuum hypothesis true?" is a question without an answer.
In a paper published Monday, Jan. 7, in the journal Nature Machine Intelligence, the researchers showed that EMX is inextricably linked to the continuum hypothesis. It turns out that EMX can solve a problem only if the continuum hypothesis is true. But if it's not true, EMX can't.. That means that the question, "Can EMX learn to solve this problem?"has an answer as unknowable as the continuum hypothesis itself.
(Excerpt) Read more at livescience.com ...
Words, words and more meaningless words.....
All right, who farted?
When math meets the number of angels that can dance on the head of a pin.
The answers are in the back of the book.
OTOH, there are infinity-deniers:
Like where are Hilliary’s emails? Yes, unknowable.
Infinity and Beyond!
It has been solved. The answer is of course, 42.
I would solve the problem but I am kind of busy today.
And in February, 2002, at a Department of Defense briefing, Donald Rumsfeld agreed:
"There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don't know. But there are also unknown unknowns. There are things we don't know we don't know."
I have a proof for this, but there’s insufficient space to show it here.
..and the last category is exponentially larger than all the others combined.
OK, so let me get a question/comment in.
Infinite means — never-ending. Goes on forever. Never stops.
So, there are infinite integers and infinite real numbers, correct?
Then, since they never stop, the point is moot. There aren’t more real numbers, because of the state of infiniteness, that never ends.
I don’t see an issue. I simply accept infinite means what it means. You can’t count to infinite, either in integers or real numbers.
Infinity + 1
Has always driven me nuts that pi is an approximation.
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