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 ...
“An Engineer, Someone that has forgotten more mathematics than you will ever know.”
I like that. I’ll put that next to ...
“Honk if you passed P-Chem.”
One of my first jobs was working for a EE, who was in his later 40s. When I met his manager for a one-on-one meeting, his direct manager in his mid-60s said, “Charlie has forgotten more than anyone here has ever known.”
Professor Jennings explains this theory to Pinto:
...“Honk if you passed P-Chem.”
P-Chem was the first class that I genuinely was getting lost in the Math
Before that, no class’ math was anything other than intuitively obvious
There is an infinite amount of things that human minds are not equipped to understand, either by Godly design or evolution, where pondering infinity is not at the top of the list for survival traits. Godel had the privilege of perceiving a lot more of what we can’t know than the average Joe. I, in my relative stupidity, see that life is not infinite, and there are better things to do with it.
So the idea of comparing "infinities" is in itself absurd. How can one "forever" be longer than another?
It is correct to say the real numbers is an unbounded (infinite) set. It is also correct to say that the integers are an unbounded set. It is not correct to say that the set of real numbers is greater than the set of integers.
Not my area of expertise, but I thought computers were based on binary system, not base ten. But I get your point.
Yes, but at any point in the count, there is more of one. So there is a difference.
For each 1 integer, there are infinity real numbers
Why 1/137??
Because otherwise my son we would not be standing here having this conversation.
Chuckles.
” Sort of looking at dazies growing ....”.
LOL ... no doubt you are qualified as an engineer ... looking at the daisies ... me too, I studdied injineerrin’ a long time ago.
” Sort of looking at dazies growing ....”.
LOL ... no doubt you are qualified as an engineer ... looking at the daisies ... me too, I studdied injineerrin’ a long time ago.
α-1 = 137.035999139 approximately
“I would contend that the older and wiser we get the more we realize that we dont know JACK.”
There is no doubt about that. It brings one to understand the meaning of humility. I took my first step in that understanding the day I graduated from grad school, realizing how little I really knew and understood. I believe John Wooden said something to the effect, “The moment you think you know everything, the most important lesson is about to begin.”
Makes sense.
I thought Gunter Zoolof solved this.
Lots of FR mathematicians up early this morning
“-Chem was the first class that I genuinely was getting lost in the Math.”
You, me and thousands of others. Back then, getting a “C” in P-Chem was good thing, and a “D” was respectable.
If numbers are basically crap we made up it is possible for there to be other crap we make up.
AS was stated in the quote: “The value of this constant, almost exactly 1/137”
This is what may be termed “literary license”.
Percent error, BTW, works out to be = 0.02628%
Human brains have a lot more horsepower than even the biggest super-computer.
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