Musings on the Impossible 1: Monument Valley, M.C. Escher, Quantum Mechanics and SF

Screenshot from Monument Valley (the game)

A year or so I bought the new game Monument Valley. I rarely play games, yet this is easily the most compelling one I tried in a long time. Dubbed as ‘an illusory adventure of impossible architecture and forgiveness’, it is heavily based on my fellow countryman M.C. Escher’s ‘Impossible Constructions’ litographs: in particular ‘Ascending and Descending’, ‘Waterfall’ (pictured below) and ‘Relativity’.

The game uses similar ‘impossible constructions’ that need to be ‘understood’ (or at least acknowledged) in order to progress to the higher levels. These constructions are basically trompe l’œil: projecting 3-dimensional images on a 2-dimensional surface. As such, it becomes possible to do things in this projected 3-D space that would not be possible in a real 3-D space. Like pillars supporting a construction that is simultaneously after and in front of it, a pathway that first passes below an aquaduct, then over it, while finally connecting to a tower that is placed at its beginning: similarly, the aquaduct passes over the pathway, then under it, and finally drops its water from its one end strainght unto its other end, from which it goes upstram again, not dissimilar from M.C. Escher’s ‘Waterfall’ (see image from the Monument Valley website, above).

So while one part of your mind might rebel against these constructions that are impossible in ‘proper’ 3-D space, a different part has to accept these impossibilities as a given, and then work with them. It reminds me, very strongly, of quantum mechanics.

In quantum mechanics, also things happen that seem impossible: particle/wave duality, shape-shifting neutrinos, the double-slit experiment (quantum interference), the uncertainty principle, entanglement, and many more. Quantum strangeness that seems incomprehensible to our everyday minds. As the renowned physicist Richard Feynman said in The Character of Physical Law: “I think I can safely say that nobody understands quantum mechanics”.

Yet, we increasingly use these characteristics of quantum mechanics: transistors, ultraprecise clocks that enable GPS, quantum cryptography, lasers, randomness generators, and, eventually, quantum computers. Basically, without quantum mechanics the computer on which I typed this could not exist, and the GPS location on your smartphone would not work.

A warped mirror-image of the Monument Valley game: theoretically, it could not work, it should not work, yet we use it to progress. As such I think both M.C. Escher’s famous lithographs and the Monument Valley game hint at something deeper lurking under consensual reality.

As mentioned, the ‘impossible constructions’ are 2-D renderings of a 3-D world (even if that 3-D world may not be the same as our everyday reality). To the best of my knowledge, there are several theories that use higher dimensions to explain the workings of quantum mechanics.

One is string theory: this—if I understand it correctly: to paraphrase Richard Feyman by way of Brian Greene who, in his book The Elegant Universe more or less implied: ‘I think it’s safe to say that nobody understands string theory, with the possible exception of Edward Witten’—basically sees elementary particles are three-dimensional ‘shadows’ or ‘condensations’ of higher-dimensional strings. How many dimensions? Even that is unclear: while some seem to have settled on ten, I’ve seen twenty-six mentioned, and eleven (M-theory) and twelve (F-theory?). One particular link between esoteric mathematics and string theory is Calabi-Yau manifolds (see image below, taken from Matt Cole’s blog),

Another one is the holographic principle, which suggest that ‘the entire universe can be seen as a two-dimensional information structure “painted” on the cosmological horizon, such that the three dimensions we observe are an effective description only at macroscopic scales and low energies’.

So, in a way (before my brain melts), elementary particles can be seen as manifestations of higher-dimensional phenomena (‘sounds’ that emerge from the ‘vibrations’ [fibrations?] of higher-dimensional strings), fundamental interactions as special cases of quantum graph lattices and the reality we observe merely as 2-D info ‘projected’ on a cosmic canvas. The latter sounds suspiciously much like what both M.C. Escher and Monument Valley were and are doing.

It suggests that the 3-D reality we observe and experience is only valid at certain scales and energies (that are stack in the middle of our everyday environment), and that outside these boundaries other rules may apply (= quantum mechanics at very small scales & [general and special] relativity at very large scales; black hole phenomena & cosmic inflation at extremely high energy/matter densities).

Looking at the true fabric of reality in this way is not only what some very bright scientists do, but is also attempted by some SF writers: to imagine the impossible, and then even extrapolate the implications. Greg Egan in particular comes to mind (Diaspora and Schild’s Ladder), as do Alastair Reynolds (Diamond Dogs), James Blish’s classic Surface Tension, Greg Bear’s Blood Music (even if more on a biological scale), Charlie Stross’s Accelerando (even if more about remaking reality to a desired different one) and several others that I’m overlooking right now (feel free to give examples in the comments). It’s what I sometimes attempt in my short fiction (“Follow Me Through Anarchy”, “Qubit Conflicts” & “The Quantum Epidemic”).

Which makes me wonder: are the fundamental particles of which we all—and our experiences of reality—are made of merely manifestations or ‘condensations’ of higher-dimensional phenomena? Do we exist in a plane of reality that is merely a minor substrate of a multi-reality so complex we can’t even begin to imagine it? Or are these approaches overtly intricate blind alleys because we don’t see the real—much simpler—solution? These are some of the thoughts that cross my mind when I’m playing Monument Valley. That alone makes it more than worth its admission price.

[More to come.]