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💠 𝕆𝔽𝔽𝕀ℂ𝕀𝔸𝕃 Post Your Interesting Stories Here

MissKitti

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INTERESTING STORIES
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**WHEN EVER YOU WANT TO RETURN TO THE MAIN MENU SIMPLY CLICK ON " " WHERE EVER YOU SEE IT TO RETURN TO THE MAIN MENU**

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MissKitti

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The Deepest Uncertainty
When a hypothesis is neither true nor false.
Nautilus
Ayalur Krishnan
ezgif.com-webp-to-jpg(46).jpg


Georg Cantor died in 1918 in a sanatorium in Halle, Germany. A pre-eminent mathematician, he had laid the foundation for the theory of infinite numbers in the 1870s. At the time, his ideas received hostile opposition from prominent mathematicians in Europe, chief among them Leopold Kronecker, once Cantor’s teacher. In his first known bout of depression, Cantor wrote 52 letters to the Swedish mathematician Gösta Mittag-Leffler, each of which mentioned Kronecker.
But it was not just rejection by Kronecker that pushed Cantor to depression; it was his inability to prove a particular mathematical conjecture he formulated in 1878, and was convinced was true, called the Continuum Hypothesis. But if he blamed himself, he did so needlessly. The debate over the conjecture is profoundly uncertain: in 1940 Kurt Gödel proved that the Continuum Hypothesis cannot be disproven (technically speaking, that the negation of the Hypothesis cannot be proven), and in 1963 Paul Cohen proved that it cannot be proven. Poor Cantor had chosen quite the mast to lash himself to.
In his first known bout of depression, Cantor wrote 52 letters to the Swedish mathematician Gösta Mittag-Leffler, each of which mentioned Kronecker.
How is it possible, though, for something to be provably neither provable nor disprovable? An exact answer would take many pages of definitions, lemmas, and proofs. But we can get a feeling for what this peculiar truth condition involves rather more quickly.
Cantor’s Continuum Hypothesis is a statement regarding sizes of infinity. To see how infinity can have more than one size, let’s first ask ourselves how the sizes of ordinary numbers are compared. Consider a collection of goats in a small forest. If there are six goats and six trees, and each goat is tethered to a different tree, then each goat and tree are uniquely paired. This pairing is called a “correspondence” between the goats and the trees. If, however, there are six goats and eight trees, we will not be able to set up such a correspondence: no matter how hard we try, there will be two trees that are goat-free.
Correspondences can be used to compare the sizes of much larger collections than six goats—including infinite collections. The rule is that, if a correspondence exists between two collections, then they have the same size. If not, then one must be bigger. For example, the collection of all natural numbers {1,2,3,4,…} contains the collection of all multiples of five {5,10,15,20,…}. At first glance, this seems to indicate that the collection of natural numbers is larger than the collection of multiples of five. But in fact they are equal in size: every natural number can be paired uniquely with a multiple of five such that no number in either collection remains unpaired. One such correspondence would involve the number 1 pairing with 5, 2 with 10, and so on.
If we repeat this exercise to compare “real” numbers (these include whole numbers, fractions, decimals, and irrational numbers) with natural numbers, we find that the collection of real numbers is larger. In other words, it can be proven that a correspondence cannot exist between the two collections.
The Continuum Hypothesis states that there is no infinite collection of real numbers larger than the collection of natural numbers, but smaller than the collection of all real numbers. Cantor was convinced, but could never quite prove it.
To see why, let’s begin by considering what a math proof consists of. Mathematical results are proven using axioms and logic. Axioms are statements about primitive mathematical concepts that are so intuitively evident that one does not question their validity. An example of an axiom is that, given any natural number (which is a primitive concept), there exists a larger natural number. This is self-evident, and not in serious doubt. Logic is then used to derive sophisticated results from axioms. Eventually, we are able to construct models, which are mathematical structures that satisfy a collection of axioms.
Crucially, any statement proven from axioms, through the use of logic, will be true when interpreted in any model that makes those axioms true.
If there are six goats and eight trees, we will not be able to set up such a correspondence: no matter how hard we try, there will be two trees that are goat-free.
It is a remarkable fact that all of mathematics can be derived using axioms related to the primitive concept of a collection (usually called a “set” in mathematics). The branch of mathematics that does this work is known as set theory. One can prove mathematical statements by first appropriately interpreting the statement in the language of sets (which can always be done), and then applying logic to the axioms of sets. Some set axioms include that we can gather together particular elements of one set to make a new set; and that there exists an infinite set.
Kurt Gödel described a model that satisfies the axioms of set theory, which does not allow for an infinite set to exist whose size is between the natural numbers and the real numbers. This prevented the Continuum Hypothesis from being dis-proven. Remarkably, some years later, Paul Cohen succeeded in finding another model of set theory that also satisfies set theory axioms, that does allow for such a set to exist. This prevented the Continuum Hypothesis from being proven.
Put another way: for there to be a proof of the Continuum Hypothesis, it would have to be true in all models of set theory, which it isn’t. Similarly, for the Hypothesis to be dis-proven, it would have to remain invalid in all models of set theory, which it also isn’t.
It remains possible that new, as yet unknown, axioms will show the Hypothesis to be true or false. For example, an axiom offering a new way to form sets from existing ones might give us the ability to create hitherto unknown sets that disprove the Hypothesis. There are many such axioms, generally known as “large cardinal axioms.” These axioms form an active branch of research in modern set theory, but no hard conclusions have been reached.
The uncertainty surrounding the Continuum Hypothesis is unique and important because it is nested deep within the structure of mathematics itself. This raises profound issues concerning the philosophy of science and the axiomatic method. Mathematics has been shown to be “unreasonably effective” in describing the universe. So it is natural to wonder whether the uncertainties inherent to mathematics translate into inherent uncertainties about the way the universe functions. Is there a fundamental capriciousness to the basic laws of the universe? Is it possible that there are different universes where mathematical facts are rendered differently? Until the Continuum Hypothesis is resolved, one might be tempted to conclude that there are.
Ayalur Krishnan is an Assistant Professor of Mathematics at Kingsborough CC, CUNY.
 
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MissKitti

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MissKitti

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The "Unleashed Universe" - where all the TV & Movie Universes meet.
==========================================
**THE UNLEASHED UNIVERSE COLLECTION**
==========================================
How The United Editors Alliance began.
------------------------------------------------------------------
Created by:
JazzyRock Pictures Australia
(aka Miss_Kitti & MissKitti)
The United Editors Alliance began with Unleashed Universe in 2014
**inspired by**
D.J BeatMaster Jazz, of Totally Wacked Productions
and his 2007-2013 story writer John Ross Normanton.
with their "Mash-Up" full length movie series, a remake of
the failed 1995 movie release of Mortal Kombat, which had major
errors in it's story, Mr Normanton had been a fan of the franchise
of Mortal Kombat since the release of the MK arcade machines,
and was a massive fan of the story of MK and it's characters story.
John knew the story flawlessly, and like millions of other people
was highly dismayed by the inaccuracy of it, however the actors
did well and should not have been so harshly judged, and I think we
all agree that to make a sequel to the movie with the one and only
Lord Rayden - the great Christopher Lambert was a tragic mistake,
but again, this is no fault of the actor who replaced him, as he too is
a very good actor, as is the actors that played Shang Tsung. BUT
Shang Tsung in movie 1 should have been an old man, and should
have been made young by Shao Khan in movie 2, not too mention....
They didn't use proper game moves in the 1st movie... then stuffed
movie 2 by adding them when they weren't in the 1st movie.
John is a great writer and decided to write down the movie and fix it
however John had no recording equipment, so he decided to find bits
of other movies he knew (this guy is a walking library on movies) while
giving MK a proper history plus a very creative and original [awesome]
future,
As a writer over the years he noticed other movies that had lost their
story along the way, so he decided to use a couple of VCR's (VHS) to
put them together, remove mistakes, and do some really clever edits-
that is where the Chronicles Of Evil came from in 2008-2013.
BeatMaster Jazz loved what he had done so much, that he decided to
remake the whole thing (using John's edits) making the sound even,
(in some cases fixing the sound as he was an audio editor) and
fixing the joins in the video on the computer (VCR's are hard to edit with)

Since then Totally Wacked Productions was forced off of youtube
(despite creating proper credits and intro's) even after making a clear
disclaimer in the video, and in the decription, and then in comments. Then-
was forced off dailymotion the same way (deleting the videos).

I decided in 2014 to start remaking the series from all the ones I
was able to download before they were removed. I then tried to find better
quality replacement footage (not easy or cheap), then in 2015
the Unleashed Universe was officially born, and....
after 2 years of begging I was able to convince BeatMaster Jazz to
join forces and help remake it properly, he was willing to help with the story
but was so disheartened by youtube and dailymotion that he was not going to
physically assist as he was over the stress of having people leave
stupid comments and having his his heart broken when videos got removed,
His devotion and passion for his videos was a rare thing in the industry, and the
video industry lost a great asset when he quit editing, but then in late 2015 he
finally agreed to come back (just to help with this) as
he was given new inspiration by my release of my Mash-Up movie series Unleashed Universe.
Since then it has undergone major development, and re-development,
to increase the picture quality, and even with all new special effects by D.J BeatMaster Jazz
and T.W Productions.
But they were still limited in the editing programs and equipment they had, and then
in 2016 LizardQueen joined the rebellion and help form "The United Editors Alliance"
(Now owns Digital Frontier Media Productions).

------------------------------------------------------------------------------------------------------
**UNLEASHED UNIVERSE**
**THE VISION!**
---------------------

The aim and vision of this series is to remove the boundaries
that separate our favorite stories from each other, and to
show how it is possible for them to co-exist, therefor...
allowing us the viewer, and indeed the story creators - to not only
merge, but also to evolve the stories beyond any previous development
to allow the stories to become timeless and limitless.
This will be the one of biggest series in history, if not the biggest.....
In fact... so big that it actually outgrows itself and later turns into ...
"The Unbound Universe' in 2018 created by LizardQueen with the
assistance of Miss_Kitti aka MissKitti (myself).
==================================================================
*UNLEASHED UNIVERSE.
**spans from the before time, .....
to the end of the Universe and time itself !**
==================================================================

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superbikemike

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hey kitty 😁
 

MissKitti

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😺 Hello mike, nice to see you my friend 💜
 
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