The 4th dimension in our case is where the 3D structures including this very Universe combine and exist within changing time frames. 4D structures can’t exist within 3D ones but 3D structures can exist in a 4D just like your drawings exist within that flat paper as lines and points but couldn’t exist in our 3D world by itself. Extra dimensions work the same, like a Matryoshka doll that loses and or gains properties the further you go.
Image: 3D projection of a tesseract undergoing a simple rotation in four dimensional space.
In mathematical physics, Minkowski space or Minkowski spacetime (named after the mathematician Hermann Minkowski) is the mathematical space setting in which Einstein’s theory of special relativity is most conveniently formulated. In this setting the three ordinary dimensions of space are combined with a single dimension of time to form a four-dimensional manifold for representing a spacetime. [**]
In physics, spacetime (also space–time, space time or space–time continuum) is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as existing in three dimensions and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions. From a Euclidean space perspective, the universe has three dimensions of space and one of time. By combining space and time into a single manifold, physicists have significantly simplified a large number of physical theories, as well as described in a more uniform way the workings of the universe at both the supergalactic and subatomic levels. [**]
But my favorite explanation of extra dimensions in general is Carl Sagan’s version. His version was based on Flatland: A Romance of Many Dimensions which is an 1884 satirical short story by Edwin Abbott Abbott:
The story is about a two-dimensional world referred to as Flatland which is occupied by geometric figures. Women are simple line-segments, while men are polygons with various numbers of sides. The narrator is a humble square, a member of the social caste of gentlemen and professionals in a society of geometric figures, who guides us through some of the implications of life in two dimensions. The Square has a dream about a visit to a one-dimensional world (Lineland) which is inhabited by “lustrous points”.
He attempts to convince the realm’s ignorant monarch of a second dimension but finds that it is essentially impossible to make him see outside of his eternally straight line.
He is then visited by a three-dimensional sphere, which he cannot comprehend until he sees Spaceland for himself. This Sphere (who remains nameless, like all characters in the novella) visits Flatland at the turn of each millennium to introduce a new apostle to the idea of a third dimension in the hopes of eventually educating the population of Flatland of the existence of Spaceland. From the safety of Spaceland, they are able to observe the leaders of Flatland secretly acknowledging the existence of the sphere and prescribing the silencing of anyone found preaching the truth of Spaceland and the third dimension. After this proclamation is made, many witnesses are massacred or imprisoned (according to caste).
After the Square’s mind is opened to new dimensions, he tries to convince the Sphere of the theoretical possibility of the existence of a fourth (and fifth, and sixth …) spatial dimension.
The depiction above is a 4 dimensional figure as represented by 3 dimensional cubes within cubes to visualize how 4th dimensions may work.
Related: Carl Sagan explains extra dimensions

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![Black Hole Firewall: Trouble On The Edge
Ever wondered what happens to things as they are consumed by the black hole, the left over matter of dead stars? For a time, it used to be okay to assume matter was destroyed once it entered into a black hole, spaghettified and all.. but it turned out that this couldn’t be further away from the truth. NewScientists Anil Ananthaswamy has a wonderful 3 page piece getting into full details of this history and what questions scientists are asking now. If you love black holes, this is a definite recommend. Although registration (completely free!) is required to view the whole article. It’s pretty insightful and accurately presents the problems currently being faced with how black holes do what they do:
“Paradoxes are good in physics,” reflects John Preskill. “They help to point the way towards important discoveries.” Quantum mechanics and Einstein’s theories of relativity offer plenty to choose from. There’s the cat that can be dead and alive at the same time. Or the Back to the Future-style time traveller who kills his own grandfather, rendering his own birth impossible. Or the twins who disagree on their age after one returns from a near light-speed trip to a neighbouring star. Each perplexing scenario forces us to examine the fine print of the problem, thereby advancing our understanding of the theory behind it. A case in point is Einstein, whose own theories came from trying to resolve the paradoxes of his time.
Image: Ring of fireSam Chivers
Now Preskill, a theoretical physicist at the California Institute of Technology in Pasadena, is scratching his head over the latest one to surface. Nicknamed the black hole firewall paradox, it comes about when you consider what happens to someone falling into a black hole.
With the nearest black hole more than 1000 light years away, the question is very much a theoretical one. Yet just by studying such a possibility, physicists are hoping to make a breakthrough in their efforts to combine general relativity and quantum mechanics into a theory of quantum gravity – one of the most intractable problems in physics today.
Black holes have long been fertile breeding grounds for paradoxes. Back in 1974, Stephen Hawking, along with Jacob Bekenstein of the Hebrew University in Jerusalem, Israel, famously showed that black holes are not entirely black. Instead, they radiate energy known as Hawking radiation comprising photons and other quantum particles – an agonisingly slow process that eventually causes the black hole to evaporate completely.
Hawking spotted a problem with this picture. The radiation seemed so random that he surmised it couldn’t carry any information about the stuff that had fallen in. So as the black hole evaporates, the information it holds must eventually disappear. Yet this is in direct conflict with a central tenet of quantum physics, which says that information cannot be destroyed. The black hole information paradox was born.
Over the decades, physicists have struggled with this paradox. Hawking thought that black holes destroyed information and the answer was to question quantum mechanics. Others disagreed. After all, Hawking’s idea came from his efforts to meld general relativity and quantum mechanics – a mathematical feat so elusive that he was forced to make approximations. Preskill even made a bet with Hawking that black holes don’t destroy information.
Several arguments suggest that Hawking was wrong. One of the most compelling comes from thinking about what happens as the evaporating black hole gets smaller and smaller. If information can’t escape or be destroyed, then more and more has to be stored in an ever-shrinking volume. But if this is the case, quantum theory says the probability for making a tiny black hole increases from virtually nothing to almost infinity wherever matter collides against matter. “You should have seen it at the Large Hadron Collider, you should have seen it at Fermilab, you should have seen it in tiny room-sized particle accelerators from the 1930s,” says Don Marolf, a theorist at the University of California in Santa Barbara (UCSB). “You should see it when you go and jump up and down on the grass.”
Obviously that hasn’t happened. The other possibility – that matter and the information it carries can leak out from a black hole – is unlikely. Any material that falls in would need to travel faster than light to escape the black hole’s fearsome gravity.
Perhaps, instead, the answer lies with the Hawking radiation itself. Maybe it isn’t so featureless. “A common reaction was that Hawking had simply been careless,” says Joseph Polchinski, also at UCSB. “It wasn’t that information was lost, it was that he hadn’t kept track of it enough.”
Yet all early efforts to do away with the paradox proved unsuccessful. “Hawking had identified a really deep problem,” says Polchinski.
As it happened, Hawking changed his mind in 2004, partly due to work by an Argentinian physicist called Juan Maldacena (see “Hawking’s change of heart”). Black holes don’t destroy information after all, he conceded. He honoured the bet he made with Preskill and presented him with an encyclopaedia of baseball, which Preskill likened to a black hole, because it was heavy and it took effort to get information out of it.
Into The Abyss..
[Full Article]](http://24.media.tumblr.com/c458af9e82f506f768d4a1c8c2479867/tumblr_mkqsgwKS6K1qbn5m1o1_500.jpg)



is a standard unit of mass in astronomy that is used to indicate the masses of other 
