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 ...
Are they all evangelical Christians?
That makes you a scientist. It allows you to pursue things that have never been understood before. That is good. I am an engineer, I am satisfied with an approximation if it can adequately be used to serve my purpose to make something useful. And make millions of them.
The various sizes of infinity is interesting but for me not very useful. Sort of looking at dazies growing on a hillside.
Math’s hard.
I need one of those to put on my office door for my typical day of dealing with the techno-challenged and intellectually lazy.
It’d be pegged on danger whenever a printer problem came up.
“That’s not without getting into Complex Numbers”
Even as a child, faced with the concept of infinity, I wondered how you could ever count to one.
Pi is not an approximation.
But they cannot be counted, or should I say enumerated, because they’re infinite.
Infinite is a state that cannot be enumerated. Logic tells us that, too.
I was wondering when someone was going to drop a cat into this mess. Thread hijacker.
bttt!
There are in fact infinitely many infinities. [No comment on which infinity is meant in that statement.]
Liberalism is like Nomad. Its Flawed Perfection.
Mental masturbation, IMHO...
Even worse is Euler's Identity
Math may be used to approximate what we accept as scientific reality quite well...but it still is a creation of our minds and is subject to our own physical limitations..It is no surprise that there are unknowables...even in a sophisticated artificial created “world” of pure math..
The probability of a printer failure is proportional to the importance of the document you are printing. The printer has a sensor in it that makes this happen.
Experienced continual observation and learning throughout life. I would contend that the older and wiser we get the more we realize that we dont know JACK.
Except for O’Crazy-O-Kotex. She knows everything.
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