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 ...
(Everyone appears to be unconscious as Kirk runs in alone.)
KIRK: Nomad? Stop what you’re doing and effect repairs on the life-support systems.
NOMAD: Stop.
KIRK: You’re programmed to obey the orders of your creator.
NOMAD: I am programmed to destroy those life-forms which are imperfect. These alterations will do so without destroying the vessel which surrounds them. It, too, is imperfect, but can be adjusted.
KIRK: Nomad, I admit that biological units are imperfect, but a biological unit created you.
NOMAD: I am perfect. I am Nomad.
KIRK: No, you’re not Nomad. You’re an alien machine. Your programming tapes have been altered.
NOMAD: You are in error. You are a biological unit. You are imperfect.
KIRK: But I am your creator.
NOMAD: You are the Creator.
KIRK: I created you?
NOMAD: You are the Creator.
KIRK: But I admit I’m imperfect. How could I have created such a perfect thing as you?
NOMAD: Answer unknown. I shall analyse.
(Spock enters, with Scott, two engineers and the requested anti-grav units)
NOMAD: Analysis complete. Insufficient data to resolve problem, but my programming is whole. My purpose remains. I am Nomad. I am perfect. That which is imperfect must be sterilised.
(The engineers remove the unconscious men and take their places at the controls.)
KIRK: Then you will continue to destroy that which thinks and lives and is imperfect?
NOMAD: I shall continue. I shall return to launch point Earth. I shall sterilise.
KIRK: You must sterilise in case of error?
NOMAD: Error is inconsistent with my prime functions. Sterilisation is correction.
KIRK: Everything that is in error must be sterilised.
NOMAD: There are no exceptions.
KIRK: Nomad, I made an error in creating you.
NOMAD: The creation of perfection is no error.
KIRK: I did not create perfection. I created error.
NOMAD: Your data is faulty. I am Nomad. I am perfect.
KIRK: I am the Kirk, the creator?
NOMAD: You are the Creator.
KIRK: You are wrong! Jackson Roykirk, your creator, is dead. You have mistaken me for him. You are in error. You did not discover your mistake. You have made two errors. You are flawed and imperfect and you have not corrected by sterilisation. You have made three errors.
NOMAD: Error. Error. Error. Examine.
KIRK: You are flawed and imperfect! Execute your prime function!
NOMAD: I shall analyse error. Analyse error,
KIRK: Now. Get those antigravs on it.
NOMAD: Examine error. Error.
(The anti-gravs are not stopped by any forcefields.)
KIRK: We’ve got to get rid of it while it’s trying to think.
SPOCK: Your logic was impeccable, Captain. We are in grave danger.
KIRK: Scotty, the transporter room.
NOMAD: Analyse error.
(Kirk and Spock carry Nomad out, followed by Scott.)
[Transporter room]
NOMAD: Error.
KIRK: Scotty, set the controls for deep space. Two ten, mark one.
SCOTT: Aye, sir.
NOMAD: Faulty!
Ready, sir?
NOMAD: Faulty!
KIRK: Nomad, you are imperfect!
NOMAD: Error. Error.
KIRK: Exercise your prime function.
NOMAD: Faulty! Faulty! Must sterilise. Sterilise,
KIRK: Now!
SCOTT: Energising.
(They observe the satisfying explosion on a monitor.)
They didn’t ask me for help. So it probably won’t ever get solved.
And how do you "know" that?
I bought a Christmas Ornament this year which says “An Engineer, Someone that has forgotten more mathematics than you will ever know.”
I actually understand what is being said. I think it was college algebra III where I learned the difference between equal and equivalent. For example, Whole numbers (0, 1, 2, …) are equivalent to the integers (…-2, -1, 0, 1, 2, …).
First time since I graduated have I used that knowledge.
Buzz Lightyear has it solved...
C’mon, Pierre. Is that where you’re going to leave us, at last?
Asimov answered The Last Question with “Let there be light.”
Mathematics version of flat Earthers...
QED
38 Then the Lord spoke to Job out of the storm. He said:
2
“Who is this that obscures my plans
with words without knowledge?
3
Brace yourself like a man;
I will question you,
and you shall answer me.
4
“Where were you when I laid the earth’s foundation?
Tell me, if you understand.
5
Who marked off its dimensions? Surely you know!
Who stretched a measuring line across it?
6
On what were its footings set,
or who laid its cornerstone—
7
while the morning stars sang together
and all the angels[a] shouted for joy?....
**********
As a scientist (and a Christian), both of them fit well together. As long as I heed Dirty Harry’s advice.
.
.
.
“A man’s got to know his limitations.”
For all practical purposes, the answer is “No.” Or is it?
Think of it this way. Between 1 and 1.1 there are an infinite set of numbers, while at the same time there are an infinite set of numbers between 1 and 1.01. Logic tells us there should be ten times as many numbers between the latter but that would mean one set of infinity is larger than another set of infinity.
We won’t know until we open the box.
https://en.wikipedia.org/wiki/Finitism
Thanks for bringing that up. It’s a legitimate disagreement unlike the flat Earth nonsense.
You must have been watching the version with British subtitles :)
I thought the article was on how my computer will on occasions shut itself down. /s
It’s impossible to compare two things that are infinite. Infinite means that you haven’t finished counting yet. When you have finished counting you can compare, but infinite means you never get to the end.
Apparently, some infinities are larger than others. Is there infinity envy?
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