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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; rafiletzter; stringtheory
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To: Uncle Lonny
I would solve the problem but I am kind of busy today.

Cuius rei demonstrationem mirabilem sane detexi hanc marginis exiguitas non caperet. [I have discovered a truly remarkable proof of this theorem which this margin is too small to contain.]

41 posted on 01/12/2019 5:58:30 AM PST by Pollster1 ("Governments derive their just powers from the consent of the governed")
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To: BenLurkin

Now you’ve done it. I’ m gonna be up all night pondering this. :-)


42 posted on 01/12/2019 5:58:46 AM PST by Vinnie
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To: BenLurkin

Thanks for the thought-provoking article.


43 posted on 01/12/2019 5:59:41 AM PST by ptsal
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To: EEGator

Loki: “We have a Hulk.”


44 posted on 01/12/2019 6:01:02 AM PST by Lazamataz (You know, when I advised Democrats to vote AFTER Nov 6th, I didn't think they'd actually DO it.)
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To: BenLurkin

Yeah. Me too.

45 posted on 01/12/2019 6:02:12 AM PST by Louis Foxwell (The denial of the authority of God is the central plank of the Progressive movement.)
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To: BenLurkin
There are an infinite # of Integers
There are an infinite # of real numbers
Between each Integer there are an infinite number of real numbers.
The # of Real Numbers is therefore Infinity * Infinity

Whats between Infinity and Infinity squared?

That's not without getting into Complex Numbers

Back to drinking my coffee

46 posted on 01/12/2019 6:02:16 AM PST by HangnJudge
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To: DoodleBob

That was great. It was just like watching it the first time.


47 posted on 01/12/2019 6:02:38 AM PST by Radix (Natural Born Citizens have Citizen parents)
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Numbers make me angry
There is like too many and stuff


48 posted on 01/12/2019 6:02:53 AM PST by dsrtsage (For Leftists, World History starts every day at breakfast)
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To: Bitman

The cat is alive! ;D


49 posted on 01/12/2019 6:02:53 AM PST by Nuc 1.1 (Nuc 1 Liberals aren't Patriots. Remember 1789!)
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To: DoodleBob

The General didn’t too well with ultimate questions either.

https://www.youtube.com/watch?v=ljGH07Unfe8


50 posted on 01/12/2019 6:04:08 AM PST by wally_bert (We're low on dimes in fun city.)
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To: EEGator

Chuckles. Just watched that. Apparently we lost completely.


51 posted on 01/12/2019 6:04:29 AM PST by Nuc 1.1 (Nuc 1 Liberals aren't Patriots. Remember 1789!)
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To: wally_bert

My favorite TV series ever!


52 posted on 01/12/2019 6:05:36 AM PST by P.O.E. (Pray for America)
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To: DoodleBob

Nomad’s programming got damaged. It didn’t discover it and it committed more errors.

Its quest for ultimate perfection resulted in its own destruction.

A perfect probe condemned by the unknowables of its own programming.

Logic itself can be undermined by the existence of paradox.


53 posted on 01/12/2019 6:05:52 AM PST by goldstategop (In Memory Of A Dearly Beloved Friend Who Lives In My Heart Forever)
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To: Bitman

Beat me to it!


54 posted on 01/12/2019 6:06:47 AM PST by Ciaphas Cain (FreeRepublic.com is the most-used app on my iPhone.)
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To: BenLurkin

Our base 10 number system is a flawed model. It has gaps everywhere that we need to just think around. Like the square root of negative one. It can’t represent PI or even 2/3. So we have invented a few patches. Some of the patches drive computers nuts, like 5/0. Computers always check to make sure that they do not divide by zero. But division is something that is unnatural to computers. They can do it, but very awkwardly. Of course multiplication or adding is very simple and fast. One day someone will come up with a better system. It may require more, or different digits. It will certainly not be based ten.

But our math does pretty good for the physical world we live.


55 posted on 01/12/2019 6:07:26 AM PST by poinq
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To: P.O.E.

One of the best ever made.


56 posted on 01/12/2019 6:08:21 AM PST by wally_bert (We're low on dimes in fun city.)
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To: Alas Babylon!
"I simply accept infinite means what it means."

Yeah but, maybe infinite doesn't mean what it means... Like, maybe this isn't Saturday... Maybe it's really Tuesday... Maybe up isn't really that, but in fact, it's down...hmmmm

57 posted on 01/12/2019 6:09:46 AM PST by unread (Joe McCarthy was right.......)
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To: wally_bert
Loved this dial

Gotta get one for my computer

58 posted on 01/12/2019 6:12:05 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: Sirius Lee

When engineering meets the number of transistors that can fit on a chip...


59 posted on 01/12/2019 6:12:31 AM PST by null and void (If they don't respect our borders, why would you expect them to respect our National Parks, or us?)
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To: BenLurkin

42


60 posted on 01/12/2019 6:13:04 AM PST by Dubh_Ghlase (Oh boy!)
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