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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: super7man

In my case, the more irrelevant the printed thing is, the more the idiot will whine about it.

Taking a stand alone printer away from some of my users when they die is almost taking the first born based on the crying.


121 posted on 01/12/2019 7:32:12 AM PST by wally_bert (We're low on dimes in fun city.)
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To: Sacajaweau
Has always driven me nuts that pi is an approximation.

Pi as a fraction is a real number not an approximation. Pi as a decimal is an irrational number and goes on infinitely, I think. If the above is true it might have to do with the mechanics of the number system we use, but I do not know how that could be.

122 posted on 01/12/2019 7:32:57 AM PST by Rapscallion (Walls work anytime night or day, any weather)
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To: Chengdu54

QED


123 posted on 01/12/2019 7:34:33 AM PST by Rio
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To: _Jim

Long term ratio of a Fibonacci sequence.
1.618...


124 posted on 01/12/2019 7:41:32 AM PST by EEGator
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To: BenLurkin

Does using a larger infinity in solving an integral make it more accurate?


125 posted on 01/12/2019 7:49:01 AM PST by Boiler Plate ("Why be difficult, when with just a little more work, you can be impossible" Mom)
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To: BenLurkin

I’m sticking with the “One Size Fits All, Infinity”.


126 posted on 01/12/2019 7:51:04 AM PST by Boiler Plate ("Why be difficult, when with just a little more work, you can be impossible" Mom)
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To: exinnj

Hillary was Right!

Math is Hard.


127 posted on 01/12/2019 7:55:19 AM PST by Boiler Plate ("Why be difficult, when with just a little more work, you can be impossible" Mom)
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To: BenLurkin

I spent a year reading Godel one day.


128 posted on 01/12/2019 8:00:15 AM PST by Ouchthatonehurt
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To: BenLurkin

There aren’t more real numbers than integers because both lists are endless. Infinity is not a number, it means ‘endless’.


129 posted on 01/12/2019 8:22:15 AM PST by Cruising Speed
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To: JohnG45
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

Known Knowns - Educated, I know what I know when I know it.

Known Unknowns - Scholarly research and study, I don't have the answer yet, but still thinking and looking for it.

Unknown Unknown - Village Idiot level of ignorance. (Democrat)

130 posted on 01/12/2019 8:34:38 AM PST by Dustoff45
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To: BenLurkin


131 posted on 01/12/2019 8:37:51 AM PST by Chode ( WeÂ’re America, Bitch!)
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To: Alas Babylon!
You can’t count to infinite, either in integers or real numbers.

Maybe not. If one can get enough taxpayer $$$'s then one can spend a lifetime trying! It beats watching the sex life of some toad.

132 posted on 01/12/2019 8:39:16 AM PST by BlackbirdSST (Con-gre$$, the biggest welfare class this country has ever produced.)
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To: MV=PY

Touché- maybe just not my cup of tea.


133 posted on 01/12/2019 8:39:49 AM PST by jagusafr
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To: BenLurkin

As soon as one blurs the distinction between continuous and discrete quantities having a coherent discussion about what infinity means becomes meaningless.

Infinity with regard to discrete quantities means that there is never a greatest, you can always add one.

Infinity with regard to continuous quantity means you can divide it in any manner you please.

In computer science the distinction between continuous and discrete quantity has been for the most part preserved.

In modern “pure” mathematics the distinction has been obscured. This causes modern mathematics to become a grotesque exercise. Anyone who has endured a graduate level course in “real analysis” can attest to the stupid proofs that claim that the real number system can be constructed, it is absurd.

You can trace this back to Nicholas Bourbaki, aka the mathematicians that Hitler chased out of Germany. Hitler was a monster, but he was right about the corruption of mathematics.


134 posted on 01/12/2019 8:41:44 AM PST by blackpacific
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To: BenLurkin

The premise is that numbers are a real thing, rather than a human construct to keep accounts in approaching an unknowable reality.


135 posted on 01/12/2019 9:00:02 AM PST by Chaguito
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To: BenLurkin

This thread explains why I hate the idea of self driving cars


136 posted on 01/12/2019 9:00:50 AM PST by Rad_J
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To: Susquehanna Patriot

Very qualified as an engineer. And I can prove it because I do not know how to spell Daisies.

Married an artist. She taught me how to appreciate the other side.


137 posted on 01/12/2019 9:03:28 AM PST by super7man (Madam Defarge, knitting, knitting, always knitting)
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To: JohnG45
This would be the 2nd category - the known unknowable...

I miss watching Donald Rumsfeld chop off the heads of ignorant reporters.

138 posted on 01/12/2019 9:03:39 AM PST by no-s (when democracy is displaced by tyranny, the armed citizen still gets to vote...)
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To: IronJack

Integers are countably infinite, real numbers are uncountably infinite. They are provably different, e.g. by Cantor’s diagonal proof. The number of rational numbers is also countable.


139 posted on 01/12/2019 9:04:48 AM PST by coloradan (The US has become a banana republic, except without the bananas - or the republic.)
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To: Chengdu54

I have a proof for this, but there’s insufficient space to show it here.”
Thank you Monsieur Fermat


140 posted on 01/12/2019 9:06:55 AM PST by Scaramouch
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