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 ...
And this is why kids don’t like math.
Used to be, physics drove math, that is, observation of nature resulted in the observation of certain relationships that were quantifiable via ‘figures’ and ‘counting’ and that became the basis for ‘math’.
Now we have the tail wagging the dog, so to speak. Math thinks it can create physics ...
If you accept infinity as a concept rather than a number, this problem is not too difficult.
Kurt Godel has the only valid answer. An infinite number cannot be said to exist until it is described.
I abused myself by reading the article before morning coffee.
the number of angels that can dance on the head of a pin.
still being asked and answered: https://forums.catholic.com/t/how-many-angels-can-dance-on-the-head-of-a-pin/251203/18
What do you have against base 10?
Won't any other base have the same problems?
I’m with your fellers...
You don't EVEN want to think about the "Fine-structure constant" then ...
“The strength of the familiar electromagnetic force between two electrons, for example, is expressed in physics in terms of a constant known as the fine structure constant. The value of this constant, almost exactly 1/137, has puzzled many generations of physicists. A joke made about the famous English physicist Paul Dirac (1902-1984), one of the founders of quantum mechanics, says that upon arrival to heaven he was allowed to ask God one question. His question was: "Why 1/137?”
― Mario Livio, The Golden Ratio: The Story of Phi, the World's Most Astonishing Number
All of this is correct, it just doesn’t matter.
Just like the points on Who’s Line is it Anyway.
It's the set of tenths. 1.0, 1.1, 1.2, etc.
Then you have the set of hundredths, thousandths, and so on.
Seems pretty obvious.
I like pecan pi......
“I simply accept infinite means what it means.”
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
Leave it to mathematicians to create a problem with no solution. I know a lot of people like this.
That said, the solution is simple. Don’t conceptualize infinity as a number or having size. That makes no logical sense. Therefore the hypothesis is false because it is based on seeing infinity as a number itself!
Is this an existential fallacy?
I have no idea what I’m talking about.
Yep, the same kind of mental masturbation Einstein did.
His mental masturbation produced the understanding of magnetism, our GPS system, explained the color of gold, why mercury is liquid at room temperature, the invention of the television, our observations of space (light bending), predicted the existence of black holes, predicted that time "slows down" with velocity, invention of the atomic bomb, etc.
>> When math meets the number of angels that can dance on the head of a pin. <<
The actual answer by Aquinas is not only NOT absurd, but absolutely foundational to the understanding of the physical world around us: things which are not composed of matter do not have volume.
Only the odd numbered ones...
GOD told us the answer himself long ago: ‘I AM that I AM”
Intuitively obvious upon casual observation.
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