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Mathematicians Discovered a Computer Problem that No One Can Ever Solve
livescience.com ^ | January 11, 2019 08:08am ET | By Rafi Letzter,

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 ...


TOPICS: Science
KEYWORDS: continuumhypothesis; kurtgodel; paulcohen; stringtheory
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1 posted on 01/12/2019 5:15:03 AM PST by BenLurkin
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To: SunkenCiv

2 posted on 01/12/2019 5:17:28 AM PST by BenLurkin (The above is not a statement of fact. It is either satire or opinion. Or both)
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To: BenLurkin

Words, words and more meaningless words.....


3 posted on 01/12/2019 5:19:03 AM PST by exinnj
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To: BenLurkin

X2


4 posted on 01/12/2019 5:19:13 AM PST by TruthWillWin ([[[MSM]]])
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To: BenLurkin

Whhhaaaaatt?


5 posted on 01/12/2019 5:19:17 AM PST by Meadow Muffin
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To: BenLurkin

All right, who farted?


6 posted on 01/12/2019 5:19:22 AM PST by ImJustAnotherOkie (All I know is what I read in the papers.)
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To: BenLurkin

When math meets the number of angels that can dance on the head of a pin.


7 posted on 01/12/2019 5:20:13 AM PST by Sirius Lee (In God We Trust, In Trump We MAGA)
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To: exinnj

….and numbers.


8 posted on 01/12/2019 5:21:28 AM PST by BenLurkin (The above is not a statement of fact. It is either satire or opinion. Or both)
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To: BenLurkin

The answers are in the back of the book.


9 posted on 01/12/2019 5:26:11 AM PST by Texas Eagle (If it wasn't for double-standards, Liberals would have no standards at all -- Texas Eagle)
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To: BenLurkin

OTOH, there are infinity-deniers:

https://en.wikipedia.org/wiki/Finitism


10 posted on 01/12/2019 5:27:42 AM PST by P.O.E. (Pray for America)
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To: BenLurkin

Like where are Hilliary’s emails? Yes, unknowable.


11 posted on 01/12/2019 5:28:23 AM PST by subterfuge (RIP T.P.)
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To: P.O.E.

Infinity and Beyond!


12 posted on 01/12/2019 5:31:19 AM PST by Tai_Chung
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To: BenLurkin

It has been solved. The answer is of course, 42.


13 posted on 01/12/2019 5:32:35 AM PST by Bitman
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To: BenLurkin

I would solve the problem but I am kind of busy today.


14 posted on 01/12/2019 5:34:06 AM PST by Uncle Lonny
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To: BenLurkin
They showed that in any mathematical system, there are certain questions that cannot be answered. They're not really difficult — they're unknowable.

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."

15 posted on 01/12/2019 5:35:06 AM PST by JohnG45
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To: BenLurkin

I have a proof for this, but there’s insufficient space to show it here.


16 posted on 01/12/2019 5:35:22 AM PST by Chengdu54
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To: JohnG45

..and the last category is exponentially larger than all the others combined.


17 posted on 01/12/2019 5:37:11 AM PST by Delta 21
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To: BenLurkin

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.


18 posted on 01/12/2019 5:37:58 AM PST by Alas Babylon! (I can always count on some FReeper to paint a dark cloud above the silver lining. --Moonman62)
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To: TruthWillWin
X2

Infinity + 1

19 posted on 01/12/2019 5:38:26 AM PST by Quality_Not_Quantity (Even my cat voted Republican)
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To: BenLurkin

Has always driven me nuts that pi is an approximation.


20 posted on 01/12/2019 5:38:40 AM PST by Sacajaweau
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