Yeah. Me too.
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 ...
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.]
Now you’ve done it. I’ m gonna be up all night pondering this. :-)
Thanks for the thought-provoking article.
Loki: “We have a Hulk.”
Yeah. Me too.
Whats between Infinity and Infinity squared?
That's not without getting into Complex Numbers
Back to drinking my coffee
That was great. It was just like watching it the first time.
Numbers make me angry
There is like too many and stuff
The cat is alive! ;D
The General didn’t too well with ultimate questions either.
https://www.youtube.com/watch?v=ljGH07Unfe8
Chuckles. Just watched that. Apparently we lost completely.
My favorite TV series ever!
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.
Beat me to it!
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.
One of the best ever made.
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
Gotta get one for my computer
When engineering meets the number of transistors that can fit on a chip...
42
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