What About Maurits Cornelis Escher?

mcescher  | Maurits Cornelis Escher (1898-1972) is one of the world’s most famous graphic artists. His art is admired by millions of people worldwide, as can be seen by the many websites on the internet.

He is born in Leeuwarden as the fourth and youngest son. After five years the family moves to Arnhem, where he spends most of his youth. After he has failed his final exam, and after a short interlude in Delft, M.C. Escher starts with his lessons in architecture at the School of Architecture and Decorative Arts in Haarlem.
Already after a week he informs his father that he wants to quit his architecture lessons and focus on studying graphic arts. He is supported in this by his teacher Samuel Jesserun de Mesquita, to whom he has shown his drawings and linocuts.

After completing his school, he travels for a long time through Italy, where he meets his wife Jetta Umiker and whom he marries in 1924. They go to Rome, where they live until 1935. During these 11 years M.C. Escher travels every year through Italy where he makes drawings and sketches that he later uses in his studio for his lithographs, woodcuts and wood engravings.

For example, the background in the lithograph Waterfall (1961) comes from his Italian period. The trees that are reflected in the woodcut Puddle(1952) are also the same trees that he uses in his woodcut Pineta by Calvi, made in 1932.

During the time that he lives and works in Italy, he makes beautiful, also more realistic works such as the Castrovalva litho in which one can see already his fascination for perspective: close, far, high and low. Likewise is the lithograph Atrani, a small town on the Amalfi coast in Italy, which he makes in 1931 and comes back in his masterpieces Metamorphosis I and II.

He is most famous for his so-called impossible drawings, such as Ascending and Descending and Relativity, but also for his metamorphoses, such as Metamorphosis I, II and III, Air and Water I and Reptiles.

During his lifetime, Escher made 448 lithographs, woodcuts and wood engravings and more than 2000 drawings and sketches. Just like some of his famous predecessors – Michelangelo, Leonardo da Vinci, Dürer and Holbein – Escher is left-handed.
In addition to his work as a graphic artist, he illustrates books, designs carpets and banknotes, stamps, murals, intarsia panels etc.
M.C. Escher is fascinated by the regular geometric figures of the wall and floor mosaics in the Alhambra, a fourteenth-century castle in Granada, Spain, which he visits in 1922 and 1936.

During his years in Switzerland and throughout the Second World War, he works with great energy on his hobby. He then makes 62 of the 137 symmetrical drawings he will make in his life. He also expands his hobby by using these symmetrical drawings for cutting wooden balls.

He plays with architecture, perspective and impossible spaces. His art continues to amaze and wonder millions of people around the world. In his work we recognize his excellent observation of the world around us and the expression of his own fantasy. M.C. Escher shows us that reality is wonderful, understandable and fascinating.

More Thinking About The Fabric Of Reality

If you look at the graphic at the top of the article (Penrose tiling) you'll notice there are a bunch of points that are centers of rotational symmetry (you can rotate it 2pi/N and get the same thing) and lines of reflection symmetry (you can mirror it over that line and get the same thing) but there is no translational symmetry (you can't slide it over in any direction and overlap with the original), this is a "quasicrystal" (in 2d)

Compare this to a grid of squares that has reflection and rotation symmetry but also has translational symmetry, this is a true "crystal" (in 2d)

This article is treating a train of laser pulses as a "1d crystal" and if long/short pulses resemble a Fibonacci sequence treating it as a "1d quasicrystal". This seems to be noteworthy in that using such a structured pulse train provides some improvements in quantum computing when it's used to read/write (i.e. shine on) information (i.e. electron configuration) from atoms / small molecules (i.e. qubits)

The "2 time dimensions" thing is basically that a N-d "quasicrystal" is usually a pretty close approximation of an [N+M]-d "true crystal" projected down into N dimensions so the considering the higher dimension structure might make things easier by getting rid of transcendental numbers etc.

They could have just said "aperiodic laser pulses" are used. No need to introduce fantastical sounding terminology about multiple time dimensions, which seems to have been done quite deliberately.

The biggest and most important step is to make sure you drop any mysticism about what a "dimension" is. It's just a necessary component of identifying the location of something in some way. More than three "dimensions" is not just common but super common, to the point of mundanity. The location and orientation of a rigid object, a completely boring quantity, is six dimensional: three for space, three for the rotation. Add velocity in and it becomes 12 dimensional; the six previous and three each now for linear and rotational velocity. To understand "dimensions" you must purge ALL science fiction understanding and understand them not as exotic, but painfully mundane and boring. (They may measure something interesting, but that "interestingness" should be accounted to the thing being measured, not the "dimension". "Dimensions" are as boring as "inches" or "gallons".)

Next up, there is a very easy metaphor for us in the computing realm for the latest in QM and especially materials science. In our world, there is a certain way in which a "virtual machine" and a "machine" are hard to tell apart. A lot of things in the latest QM and materials science is building little virtual things that combine the existing simple QM primitives to build new systems. The simplest example of this sort of thing is a "hole". Holes do not "exist". They are where an electron is missing. But you can treat them as a virtual thing, and it can be difficult to tell whether or not that virtual thing is "real" or not, because it acts exactly like the "virtual" thing would if it were "real".

In this case, this system may mathematically behave like there is a second time dimension, and that's interesting, but it "just" "simulating" it. It creates a larger system out of smaller parts that happens to match that behavior, but it doesn't mean there's "really" a second time dimension.

The weird and whacky things you hear coming out of QM and materials science are composite things being assembled out of normal mundane components in ways that allow them to "simulate" being some other interesting system, except when you're "simulating" at this low, basic level it essentially is just the thing being "simulated". But there's not necessarily anything new going on; it's still electrons and protons and neutrons and such, just arranged in interesting ways, just as, in the end, Quake or Tetris is "just" an interesting arrangement of NAND gates. There's no upper limit to how "interestingly" things can be arranged, but there's less "new" than meets the eye.

Unfortunately, trying to understand this through science articles, which are still as addicted as ever to "woo woo" with the word dimensions and leaning in to the weirdness of QM and basically deliberately trying to instill mysticism at the incorrect level of the problem. (Personally, I still feel a lot of wonder about the world and enjoy learning more... but woo woo about what a "dimension" is is not the place for that.) 

The Universe As A Holographic Quasicrystalline Tensor Network

ncatlab |  The AdS-CFT correspondence at its heart is the observation (Witten 98, Section 2.4) that the classical action functionals for various fields coupled to Einstein gravity on anti de Sitter spacetime are, when expressed as functions of the asymptotic boundary-values of the fields, of the form of generating functions for correlators/n-point functions of a conformal field theory on that asymptotic boundary, in a large N limit.

This is traditionally interpreted as a concrete realization of a vague “holographic principle” according to which quantum gravity in bulk spacetimes is controlled, in one way or other, by “boundary field theories” on effective spacetime boundaries, such as event horizons. The original and main motivation for the holographic principle itself was the fact that the apparent black hole entropy in Einstein gravity scales with the area of the event horizon instead of the black hole’s bulk volume (which is not even well-defined), suggesting that gravity encodes or is encoded by some boundary field theory associated with horizons; an idea that, in turn, seems to find a concrete realization in open/closed string duality in the vicinity of, more generally, black branes. The original intuition about holographic black hole entropy has meanwhile found remarkably detailed reflection in (mathematically fairly rigorous) analysis of holographic entanglement entropy, specifically via holographic tensor networks, which turn out to embody key principles of the AdS/CFT correspondence in the guise of quantum information theory, with concrete applications such as to quantum error correcting codes.

quantumgravityresearch |  Recent advances in AdS/CFT holography have found an analogue in discrete tensor networks of qubits. The {5,4} hyperbolic tiling allows for topological error correction. We review a simple 32 x 32 Hamiltonian from five maximally entangled physical qubits on the boundary edges of a pentagon, whose two-fold degenerate ground state leads to an emergent logical qubit in the bulk. The inflation rule of a holographic conformal quasicrystal is found to encode the holographic code rate that determines the ratio of logical qubits to physical qubits. Generalizing SU(2) qubits to twistors as conformal spinors of SU(2,2), an H3-symmetric 5-compound of cuboctahedral A3 = D3 root polytopes is outlined. Motivated by error correction in the Hamming code, the E8 lattice is projected to the H4-symmetric quasicrystal. The 4-dimensional 600-cell is found to contain five 24-cells associated with the D4 root polytope associated with Spin(4,4). Intersection with Sp(8,R) phase space identifies three generations of conformal symmetry with an axial U(1) symmetry. A lightning review of E8(-24) phenomenology with Spin(12,4) is pursued for gravity and the standard model with a notion of CDT-inspired discretized membranes in mind. Warm dark matter beyond the standard model is briefly articulated to stem from intersecting worldvolumes related to the Leech lattice associated with the Golay code, hinting at a monstrously supersymmetric M-theory in D=26+1. A new D=27+3 superalgebra is shown to contain membranes that can give a worldvolume description of M-theory and F-theory.