As an abstract term, "infinity" or "infinite" is correct, if ambiguous. When using the Marvel take on it by saying that there are multiple levels of infinity because a series of progressing numbers to infinity should logically have a larger set of numbers than a similar progression of even numbers, it becomes incorrect. Infinity itself is not a number, but rather an indefinitely extending process. This makes it logically meaningless and paradoxical to have half of an infinite process.
In comics, using such terms as hyperbole is fine. It is incorrect to assume Marvel's definition though, even if I understand their rationale.
Edit: While there are indeed different classes of infinity in a mathematical sense (set theory etc), it still doesn't make assumptions as to whether a certain set is > another.
Originally posted by OualladaTo me a fraction of infinity isnt infinity. But comic book writers sometimes make us scratch our heads trying to understand their intentions.
I know this happened on panel, and was used to explain the flagrant usage of hyperbole in comics, but there isn't really such a thing as a fraction of infinity.
Originally posted by OualladaAs an abstract term, "infinity" or "infinite" is correct, if ambiguous.
When using the Marvel take on it by saying that there are multiple levels of infinity
because a series of progressing numbers to infinity
should logically have a larger set of numbers than a similar progression of even numbers,it becomes incorrect.
Marvel's claim of levels of Infinity wasn't made up by Marvel,
it's actually based on a real theorem from the real world created by Georg Cantor.
This theorem has been widely accepted as a legitimate theorem since 1891,
even inducted into Princeton's curriculum (like Calculus)
http://en.wikipedia.org/wiki/Cantor%27s_theorem
Cantor's Theorem:
"The theorem is named for Georg Cantor, who first stated and proved it."
As you can see, Marvel literally even uses his name.
=====================================
Originally posted by Mr Master
Marvel's claim of levels of Infinity wasn't made up by Marvel,
it's actually based on a real theorem from the real world created by Georg Cantor.This theorem has been widely accepted as a legitimate theorem since 1891,
even inducted into Princeton's curriculum (like Calculus)http://en.wikipedia.org/wiki/Cantor%27s_theorem
Cantor's Theorem:
"The theorem is named for Georg Cantor, who first stated [B]and proved it
."As you can see, Marvel literally even uses his name.
===================================== [/B]
Actually, Cantor's theorem was more of a philosophical argument than a mathematical one, and was derived to give the mathematical world an attainable infinity, in a nutshell. It may or may not hold true under all mathematical rules, but that has never stopped theorems from being inducted to the syllabus before. Descartes was destroyed by Nietzsche. Doesn't stop the cogito from being part of philosophy texts today either.
I'm not sure if you understand cantor's theorem and set theory well, but from what I understand, Cantor's theorem has many detractions indeed:
1) Formal conclusions reached via abstractions need to be translated back into real-world assertations. With computers providing a concrete mathematical base, the world of computations needs to be real and concrete as well, while Cantor's theorem gives us infinite sets and power sets of infinite sets. Useful, but ultimately fictional. Imaginary numbers are a good example here.
2) The rules of inference for abstractions have it that any statement about the infinite should have implications for approximations to the infinite.
3) Quotes from mathematicians and fellow philosophers:
"classical logic was abstracted from the mathematics of finite sets and their subsets...Forgetful of this limited origin, one afterwards mistook that logic for something above and prior to all mathematics, and finally applied it, without justification, to the mathematics of infinite sets. This is the Fall and original sin of [Cantor's] set theory ..." (Weyl, 1946)
"We cannot use the modern axiomatic method to establish the theory of sets. We cannot, in particular, simply employ the machinery of modern logic, modern mathematical logic, in establishing the theory of sets" (Mayberry 2000, 7)
"Classical mathematics concerns itself with operations that can be carried out by God.. Mathematics belongs to man, not to God... When a man proves a positive integer to exist, he should show how to find it. If God has mathematics of his own that needs to be done, let him do it himself." (Errett Bishop (1967))
Basically, the big fuss is about whether or not true infinity exists, and that if Cantor were to argue for its existence (which the theories that you brought up are all linked to), he should be able to approximate such a number.
Originally posted by OualladaActually, Cantor's theorem was more of a philosophical argument than a mathematical one, and was derived to give the mathematical world an attainable infinity, in a nutshell.
Also, Marvel gives us on panel that portion of Cantor's theorem:
In Marvel, there are different levels of infinity: (omnipotence)
(based on Cantor's theorem)
Kubik says,
"Our power is as nothing to the Celestials"
Kosmos replies,
"But Kubik, do we not possess Infinite Power (Omnipotence)
Kubik retorts,
"Yes, Our might is Infinite. But there are Levels of Infinity"
..............................................................
CONTINUES ...
Kubik finishes:
"Thus are demonstrated two levels of infinity,
there are of course, an infinite number more"
..............................................................
Dr Strange corroborates this Marvel fact:
"the very Concept of Infinity is relative,
Numbers are Infinite, so are odd Numbers, yet by definition,
there are Twice as many Numbers as there are odd Numbers ...
One Infinity is included within a larger Infinity"
=====================================
Originally posted by OualladaIt may or may not hold true under all mathematical rules, but that has never stopped theorems from being inducted to the syllabus before. Descartes was destroyed by Nietzsche. Doesn't stop the cogito from being part of philosophy texts today either.
I'm not sure if you understand cantor's theorem and set theory well, but from what I understand, Cantor's theorem has many detractions indeed:
1) Formal conclusions reached via abstractions need to be translated back into real-world assertations. With computers providing a concrete mathematical base, the world of computations needs to be real and concrete as well, while Cantor's theorem gives us infinite sets and power sets of infinite sets. Useful, but ultimately fictional. Imaginary numbers are a good example here.
2) The rules of inference for abstractions have it that any statement about the infinite should have implications for approximations to the infinite.
3) Quotes from mathematicians and fellow philosophers:
"classical logic was abstracted from the mathematics of finite sets and their subsets...Forgetful of this limited origin, one afterwards mistook that logic for something above and prior to all mathematics, and finally applied it, without justification, to the mathematics of infinite sets. This is the Fall and original sin of [Cantor's] set theory ..." (Weyl, 1946)
"We cannot use the modern axiomatic method to establish the theory of sets. We cannot, in particular, simply employ the machinery of modern logic, modern mathematical logic, in establishing the theory of sets" (Mayberry 2000, 7)
"Classical mathematics concerns itself with operations that can be carried out by God.. Mathematics belongs to man, not to God... When a man proves a positive integer to exist, he should show how to find it. If God has mathematics of his own that needs to be done, let him do it himself." (Errett Bishop (1967))
Basically, the big fuss is about whether or not true infinity exists, and that if Cantor were to argue for its existence (which the theories that you brought up are all linked to), he should be able to approximate such a number.
Just pointing out that Marvel did not invent this theory out of the air,
it's based on a theorem that's as widely accepted as the theorem of Calculus.
That's all.
Originally posted by Mr Master
Actually, the mathematical formula based on the theorem is included.Also, Marvel gives us on panel that portion of Cantor's theorem:
In Marvel, there are different levels of infinity: (omnipotence)
(based on Cantor's theorem)
Kubik says,
"Our power is as nothing to the Celestials"
Kosmos replies,
"But Kubik, do we not possess Infinite Power (Omnipotence)
Kubik retorts,
"Yes, Our might is Infinite. But [B]there are Levels of Infinity
"..............................................................
CONTINUES ...
Kubik finishes:
"Thus are demonstrated two levels of infinity,
there are of course, an infinite number more"
..............................................................
Dr Strange corroborates this Marvel fact:
"the very Concept of Infinity is relative,
Numbers are Infinite, so are odd Numbers, yet by definition,
there are Twice as many Numbers as there are odd Numbers ...
One Infinity is included within a larger Infinity"
=====================================
I wasn't trying to prove whether it's right or wrong, or makes sense or not.
Just pointing out that Marvel did not invent this theory out of the air,
it's based on a theorem that's as widely accepted as the theorem of Calculus.That's all. [/B]
It makes sense if you reject infinity as being abstract. It's just that it isn't really mathematically accepted nor correct, as with all unrefined philosophy.
Other than that, fair play.
Originally posted by OualladaIt makes sense if you reject infinity as being abstract.
It's just that it isn't really mathematically accepted nor correct,
as with all unrefined philosophy.
It's also definitely not just a philosophical theory either,
there's clearly a formula that supposedly proves Cantor's theorem.
http://en.wikipedia.org/wiki/Cantor%27s_theorem
Don't know if you overlooked that,
but it's not fair if the only segment of the link you went to
was the other link that leads to the perspective of those that disagree with his theorem.
I mean,
there's another side to that coin that not only agree,
but in fact,
they promote Cantor's theorem as a legitimate formula to be taken seriously.
................................................................................................................
Georg Cantor - Encyclopedia Britannica:
"German mathematician who founded set theory
and introduced the mathematically meaningful concept of transfinite numbers,
indefinitely large but distinct from one another."
http://www.britannica.com/eb/article-9020082/Georg-Cantor
................................................................................................................
Georg Cantor - Honerary member of the London Mathematical Society:
http://www-groups.dcs.st-and.ac.uk/~history/Societies/LMSHonorary.html
................................................................................................................
Georg Cantor - the prestigious PRINCETON University website:
"One of the greatest revolutions in mathematics occurred
when Georg Cantor (1845-1918)
promulgated his theory of transfinite sets."
http://press.princeton.edu/titles/4740.html
................................................................................................................
Georg Cantor - Applet--Magic.com
(site dedicated to Physics-Mathematics-Statistics)
"Georg Cantor's achievement in mathematics was outstanding.
He revolutionized the foundation of mathematics with set theory.
Set theory is now considered so fundamental,
that it seems to border on the obvious,
but at its introduction it was controversial and revolutionary.
The controversial element centered around the problem
of whether infinity was a potentiality or could be achieved.
Before Cantor,
it was generally felt that infinity as an actuality did not make sense;
one could only speak of a variable increasing,
without bound as that variable going to infinity.
Cantor not only found a way to make sense out an actual,
as opposed to a potential, infinity,
but showed that there are different orders of infinity"
http://www.sjsu.edu/faculty/watkins/cantorth.htm
................................................................................................................
Georg Cantor - Exploratorium
"In the years 1871-1884 Georg Cantor invented the theory of infinite sets."
http://www.exploratorium.edu/turbulent/CompLexicon/settheory.html
................................................................................................................
Georg Cantor - Even scholarships are given in this guys name. 🙂
"Historians of mathematics can only be grateful,
for the effort Professor Dauben has expended,
to create the synthesis of Cantor scholarship found in this book.
But the book can, and I hope will,
be read with profit by a far more extensive audience.
Any student, mathematician, philosopher, theologian, or general historian,
with an interest in Georg Cantor,
and the wondrous revolution in mathematical and philosophical thought
that his work did so much to precipitate will find this book of considerable interest."
--Thomas Hawkins, Historia Mathematica.
One of the greatest revolutions in mathematics occurred,
when Georg Cantor (1845-1918)
promulgated his theory of transfinite sets."
http://www.erraticimpact.com/~19thcentury/html/cantor.htm
................................................................................................................
Georg Cantor - "The Man who counted beyond Infinity"
Engines of Ingenuity by John Lienhard, at the University of Houston:
"By the time he was done,
Cantor had invented what we call the transfinite numbers --
numbers that go beyond infinity.
And to do that he'd had to invent set theory.
And set theory has become a building block of modern mathematics."
http://uh.edu/engines/epi1484.htm
...............................................................................................................
Just sayin.
Originally posted by King KandyYes and no. Technically speaking, the Source is not bound by anything [or at least it wasn't, before DotNG] it is simply, infinite power. And while the 'gog may be able to do anything one can imagine [it's raw power being theoretically equal to the Source] it is still bound by just that - the imagination of the one using it.
So According to you Worlogog is equal to the source?
Same could be said about the IG, I suppose - imagination is it's only real limitation. ermm
Originally posted by OualladaIf I wanted to debate things in the 'real' sense, I certainly wouldn't be posting in the comic forums. 😛
I know this happened on panel, and was used to explain the flagrant usage of hyperbole in comics, but there isn't really such a thing as a fraction of infinity.
Originally posted by Mr Master
Just cause a few mathematicians didn't agree with it,
doesn't mean it's not accepted.It's also definitely not just a philosophical theory either,
there's clearly a formula that supposedly proves Cantor's theorem.http://en.wikipedia.org/wiki/Cantor%27s_theorem
Don't know if you overlooked that,
but it's not fair if the only segment of the link you went to
was the other link that leads to the perspective of those that disagree with his theorem.I mean,
there's aanother side to that coin that not only agree,
but in fact,
they promote Cantor's theorem as a legitimate formula to be taken seriously.................................................................................................................
Georg Cantor - [B]Encyclopedia Britannica
:"German mathematician who founded set theory
and introduced the mathematically meaningful concept of transfinite numbers,
indefinitely large but distinct from one another."http://www.britannica.com/eb/article-9020082/Georg-Cantor
................................................................................................................
Georg Cantor - Honerary member of the London Mathematical Society:
http://www-groups.dcs.st-and.ac.uk/~history/Societies/LMSHonorary.html
................................................................................................................
Georg Cantor - the prestigious PRINCETON University website:
"One of the greatest revolutions in mathematics occurred
when Georg Cantor (1845-1918)
promulgated his theory of transfinite sets."http://press.princeton.edu/titles/4740.html
................................................................................................................
Georg Cantor - Applet--Magic.com
(site dedicated to Physics-Mathematics-Statistics)
"Georg Cantor's achievement in mathematics was outstanding.
He revolutionized the foundation of mathematics with set theory.
Set theory is now considered so fundamental,
that it seems to border on the obvious,
but at its introduction it was controversial and revolutionary.
The controversial element centered around the problem
of whether infinity was a potentiality or could be achieved.Before Cantor,
it was generally felt that infinity as an actuality did not make sense;
one could only speak of a variable increasing,
without bound as that variable going to infinity.Cantor not only found a way to make sense out an actual,
as opposed to a potential, infinity,
but showed that there are different orders of infinity"http://www.sjsu.edu/faculty/watkins/cantorth.htm
................................................................................................................
Georg Cantor - Exploratorium
"In the years 1871-1884 Georg Cantor invented the theory of infinite sets."
http://www.exploratorium.edu/turbulent/CompLexicon/settheory.html
................................................................................................................
Georg Cantor - Even scholarships are given in this guys name. 🙂
"Historians of mathematics can only be grateful,
for the effort Professor Dauben has expended,
to create the synthesis of Cantor scholarship found in this book.
But the book can, and I hope will,
be read with profit by a far more extensive audience.Any student, mathematician, philosopher, theologian, or general historian,
with an interest in Georg Cantor,
and the wondrous revolution in mathematical and philosophical thought
that his work did so much to precipitate will find this book of considerable interest."
--Thomas Hawkins, Historia Mathematica.
One of the greatest revolutions in mathematics occurred,
when Georg Cantor (1845-1918)
promulgated his theory of transfinite sets."http://www.erraticimpact.com/~19thcentury/html/cantor.htm
................................................................................................................
Georg Cantor - "The Man who counted beyond Infinity"
Engines of Ingenuity by John Lienhard, at the University of Houston:
"By the time he was done,
Cantor had invented what we call the transfinite numbers --
numbers that go beyond infinity.
And to do that he'd had to invent set theory.
And set theory has become a building block of modern mathematics."http://uh.edu/engines/epi1484.htm
...............................................................................................................
Just sayin. [/B]
I'm not going to indulge in a situation in which we both find quotes to substantiate a position. Those that I have provided are sound general rules of mathematics which none of yours have refuted thus far. That Cantor's theorem is at least partially philosophical in nature is indisputable, as there is no mathematical number for infinity. Without theorising infinity, it is impossible to compare an infinite set with another. I suggest you google up the philosophical portions of the theorem before suggesting otherwise.
Here is a paper written on the flaws of Cantor's theorem:
http://www.dataweb.nl/~cool/Papers/ALOE/2007-07-29-OnCantorsTheorem.pdf
As for scholarly accolades, I would bet my last dollar that Descartes has more attributed to his name than Cantor. Doesn't mean his cogito was correct either. The entire point of philosophy is to expand on unorthodox lines of thinking, flawed or otherwise.
If I may, do you have the slightest understanding of Cantor's theories and the counterarguments? If you do, I would like your take on them, not quotes of the man's accolades. If not, then I guess you have made your point on marvel using Cantor's theorems, but that you aren't really in a position to argue for or against the validity of said usage.
Originally posted by OualladaI'm not going to indulge in a situation in which we both find quotes to substantiate a position. Those that I have provided are sound general rules of mathematics which none of yours have refuted thus far. That Cantor's theorem is at least partially philosophical in nature is indisputable, as there is no mathematical number for infinity. Without theorising infinity, it is impossible to compare an infinite set with another. I suggest you google up the philosophical portions of the theorem before suggesting otherwise.
Here is a paper written on the flaws of Cantor's theorem:
As for scholarly accolades, I would bet my last dollar that Descartes has more attributed to his name than Cantor. Doesn't mean his cogito was correct either. The entire point of philosophy is to expand on unorthodox lines of thinking, flawed or otherwise.
You exclusively brought out the cats that disagree,
I provided the other perspective when other cats agree.
Originally posted by OualladaIf I may, do you have the slightest understanding of Cantor's theories and the counterarguments? If you do, I would like your take on them, not quotes of the man's accolades. If not, then I guess you have made your point on marvel using Cantor's theorems, but that you aren't really in a position to argue for or against the validity of said usage.
I'm here to debate comics, Marvel cosmology related preferably.
My point from the beginning ws and still is,
Marvel did not create the idealism of "levels of infinity"
it is based on a real world theorem that's accepted by Princeton University
like the theorem of Calculus.
That is all.
Originally posted by Mr Master
Again, just presenting the other side of the coin.You exclusively brought out the cats that disagree,
I provided the other perspective when other cats agree.I'm here to prove whether or not Cantor's theory is true, false or sensible.
I'm here to debate comics, Marvel cosmology related preferably.
My point from the beginning ws and still is,
Marvel did not create the idealism of "levels of infinity"
it is based on a real world theorem that's accepted by Princeton University
like the theorem of Calculus.That is all.
I didn't just bring up the "cats" that agree. I brought up real reasons why Cantor's theory is mathematically flawed, some in the form of quotes. Telling me about Cantor's accolades and insisting that it is non-philosophical does absolutely nothing for me.
You're here to debate Marvel cosmology, fair enough. As in my previous post, I've already mentioned that you have stated your point that marvel used said theories. As for whether the theory is true/false/logical, I see absolutely no need for the inundation of accolades, as well as a plethora of quotes that were on a subject that you don't want to debate, and which you would probably be out of your depth debating.
I don't think I ever stated that marvel created that theory. I stated that it was Marvel's take on the subject, which it evidently was, and I am saying that it isn't mathematically or philosophically perfect.
That's all she wrote.
Originally posted by OualladaI didn't just bring up the "cats" that agree. I brought up real reasons why Cantor's theory is mathematically flawed, some in the form of quotes. Telling me about Cantor's accolades and insisting that it is non-philosophical does absolutely nothing for me.
You're here to debate Marvel cosmology, fair enough. As in my previous post, I've already mentioned that you have stated your point that marvel used said theories. As for whether the theory is true/false/logical, I see absolutely no need for the inundation of accolades, as well as a plethora of quotes that were on a subject that you don't want to debate
No harm done.
Originally posted by Oualladaand which you would probably be out of your depth debating.
Let's not try to judge (or guess) the depths of my or anyone's debating format,
that's off-topic, and bordering on getting personal.
Anyway, if you're interested,
it's more like out of my present interest.
Originally posted by OualladaI don't think I ever stated that marvel created that theory. I stated that it was Marvel's take on the subject, which it evidently was, and I am saying that it isn't mathematically or philosophically perfect.
That's all she wrote.
Originally posted by Mr Master
Well, you agree with those that found "flaws" in it,
I agree with those that accepted it as a legitimate theorem like Calculus.
I do not reject the theorem, simply state that there are flaws. The two are not mutually exclusive.
Originally posted by Mr MasterA bit presumptious no?
Let's not try to judge (or guess) the depths of my or anyone's debating format,
that's off-topic, and bordering on getting personal.
Seeing as you have shown no understanding of said theorem save quoting accolades, which I personally found to be demeaning for a person who isn't interested in talking about the man's awards, but the validity of his theory, and the fact that you couldn't grasp the fact that the theory was mathematical philosophy gives me a solid enough base for assumption. Of course, I fully apologise if you DO know more about this than you are letting on. However, seeing as you seemed to underestimate my knowledge on this matter (decent at least), which is about as personal as I got with you, I await reciprocation.
Originally posted by Mr Master
Wonderful.
I get that a lot.
Originally posted by OualladaI do not reject the theorem, simply state that there are flaws.
The two are not mutually exclusive.
Originally posted by OualladaSeeing as you have shown no understanding of said theorem save quoting accolades, which I personally found to be demeaning for a person who isn't interested in talking about the man's awards, but the validity of his theory, and the fact that you couldn't grasp the fact that the theory was mathematical philosophy gives me a solid enough base for assumption.
Originally posted by OualladaOf course, I fully apologise if you DO know more about this than you are letting on. However, seeing as you seemed to underestimate my knowledge on this matter (decent at least), which is about as personal as I got with you, I await reciprocation.
Marvel has committed to the widely accepted (since 1891) real world theorem created by Cantor.
That's it.
So, Marvel has levels of infinity, that's a fact, and that's all she can write. 🙂
Originally posted by OualladaI get that a lot.
Originally posted by Mr Master
Cool. It's still part of the curriculum of prestigious Universities like Princeton.
Never said it wasn't. I don't see the need for repetition.
Originally posted by Mr Master
Whatever you say.
Correct.
Originally posted by Mr Master
My response is simple.Marvel has committed to the widely accepted (since 1891) real world theorem created by Cantor.
That's it.
Which I have previously stated. I really don't see why you took more than 5 posts to reconcile the two.
Originally posted by Mr Master
So, Marvel has levels of infinity, that's a fact, and that's all she can write. 🙂
Which I have also already stated. Read above for my thoughts.
Originally posted by Mr Master
Likewise.
Empowerment by association.
In any case, I don't think we have much more to discuss here. As mentioned, anything you felt was personal wasn't meant that way. Cool?
Originally posted by Galan007
Yes and no. Technically speaking, the Source is not bound by anything [or at least it wasn't, before DotNG] it is simply, infinite power. And while the 'gog may be able to do anything one can imagine [it's raw power being theoretically equal to the Source] it is still bound by just that - the imagination of the one using it.