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String Theory Meets Einstein - As a quick intro, here's a concise lede from the final paragraph of the OP: "Hawking [et al...] have found a way to produce expanding, accelerating universes using a negative cosmological constant. This means that string theory may, after all, describe the universe that we observe."
via +Wade Aaron Inganamort
Stephen Hawking has a big new idea: His 'Escher-verse' could be a theory of everything

Stephen Hawking has come up with a way to describe the universe that suggests it may have the same geometry as mind-boggling images by M. C. Escher

The universe may have the same surreal geometry as some of art's most mind-boggling images. That's the upshot of a study by the world's most famous living scientist, Stephen Hawking of the University of Cambridge.

The finding may delight fans of Dutch artist M. C. Escher, but Hawking's team claim that their study provides a way to square the geometric demands of string theory, a still-hypothetical "theory of everything", with the universe we observe.

Their calculations rely on a mathematical twist that was previously considered impossible. If it stands up, it could explain how the universe emerged from the big bang and unite gravity and quantum mechanics.

"We have a new route towards constructing string theory models of our world," says Hawking's colleague Thomas Hertog of the Institute for Theoretical Physics at the Catholic University of Leuven (KUL) in Belgium.

On the face of it, the idea that Escher's images can describe the layout of the universe seems to contradict what we know about it.

The images in question are tessellations, arrangements of repeated shapes, such as the images of interlocking bats and angels seen in Circle Limit IV. Although these are flat, they serve as "projections" of an alternative geometry called hyperbolic space, rather like a flat map of the world is a projection of a globe. For example, although the bats in the flat projection appear to shrink at an exponential rate at the edges, in hyperbolic space they are all the same size. These distortions in the projection arise because hyperbolic space cannot lie flat. Instead, it resembles a twisting, wiggly landscape of saddle-like hills.
That is not what our universe seems to look like. Measurements of the cosmic microwave background - the echo of the big bang - and distances to supernovae have revealed that our universe is flat, not twisted.

It is also expanding at an accelerating rate, because of a mysterious entity known as dark energy. We don't know what dark energy is or where it came from, but the mathematical language provided by Einstein's theory of general relativity has a way to describe this accelerated expansion. Sticking a constant - known as the cosmological constant - into the general-relativity equations keeps the universe expanding forever, but only if the constant has a positive sign. Until now, saying we live in an ever-expanding universe has been the same as saying our universe has a positive cosmological constant.

There are some outstanding problems, however. General relativity covers this aspect of the universe, but it can't describe the big bang. Nor can it unite gravity, which works on large scales, with quantum mechanics, which works on very small scales. "That means you cannot predict why we live in the universe that we live in," Hertog says.

String theory, in the meantime, offers a beautifully complete picture of the universe's history and connects gravity to quantum mechanics - but is most comfortable in a universe with a negatively curved, Escher-like geometry and with a negative cosmological constant.

This left physicists with a deep chasm to cross: on one side is a universe that works but lacks a complete theory, and on the other is a complete theory that doesn't describe the actual universe.

Now, Hawking, Hertog and James Hartle of the University of California, Santa Barbara, are proposing a bridge. They have found a way to produce expanding, accelerating universes using a negative cosmological constant. This means that string theory may, after all, describe the universe that we observe. The proposal grew from an idea that Hawking and Hartle had in the 1980s to get around general relativity's shortcomings by looking for a quantum picture of cosmology.
rest of the article:
Russell Davison's profile photoErik Swiger's profile photoLeo Vuyk's profile photoMarc Paul Rubin's profile photo
I'm always interested in fresh ideas. Who says that we can only describe things as A to Z, a to z, 0 to 9, circle, square, triangle, wave, red, orange, yellow, green blue, indigo, violet, (, /, x, +, -? 
Escher's artwork lends itself to being grasped intuitively, at least on a superficial level. Similarly with Bach's music. However, I've been struggling to fully understand the book, "Godel, Escher, Bach: The Eternal Golden Braid" ever since it was published.
I'm a fan of Escher's work, but this book about the Golden Braid, what is it?  Where do I get it?
It's a classic Erik, presumably you can Quack it via #DuckDuckGo , or Google if you must ;-> Way past time for sleep here, though please do follow up here if you have any trouble finding it.
Thanks +Leo Vuyk, for citing this post on your blog. Actually it might be more appropriate to cite the original post <> However, if you prefer my more concise lede, then I would appreciate having my first name spelled correctly: Mark Marc ;-> As to your question:
Will definitely read the blog post in depth, when I get control of a splitting headache :-| Looks like a great site!
+Marc Paul Rubin I don't want to go off on a tangent, but where is your name misspelled?  I don't see that anywhere on this thread. 
Erik, the misspelling is in the blog post by +Leo Vuyk, cited in his comment above. The name appears as if in lights up on a Broadway billboard ;->
Any publicity is good publicity?  (cough)
Thanks Marc, I am not a good reader and wasn't aware of Gamze Dogan's relation to the subject.
You're welcome Leo, and thanks for the correction on your blog. Have been challenged by the French spelling of my first name all my life, not to mention a common misspelling of my last name, associated with a popular sandwich ;-> For several years I also used a French-style hyphen between my first and middle names; that caused continual confusion with both computers and Human-Americans, so had to give it up. Anyway:
Got rid of my headache last night, caught up on sleep, and now have your blog post open in another Firefox tab. Looking forward to diving in this morning.
BTW +Erik Swiger, there's now a bright-red, "Breaking news" lead-in to the story there. Feels like I'm back living in New York City.
OK +Leo Vuyk, as you predict, "Pffff [...] this is all too much at once for me." ;-> The blog post seems very speculative, even in the context of theoretical physics. Is there a reference which directly (and concisely) supports the view that our universe is not expanding? Thanks!
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