“Mathematicians,” wrote M.C. Escher in a 1958 essay, “have opened the gate leading to an extensive domain, but they have not entered this domain themselves. By their very nature they are more interested in the way in which the gate is opened than in the garden lying behind it.”

In the more than 170 works now showing at the Bunkamura Museum of Art in Shibuya, the garden of Escher’s imagination spreads before us. It is an Eden of optical innocence and experience, in which the artist draws the impossible — a circular stairway that goes neither up nor down (“Ascending and Descending,” 1960), a ladder that is simultaneously both inside and outside a building (“Belvedere,” 1961).

Planes are disjointed, dimensions distorted and space folds in on itself. Things both are and are not what they seem — rather like the home of this fine collection, Huis Ten Bosch, a picture-perfect Dutch town built in Nagasaki Prefecture as a tourist attraction.

Maurits Cornelis Escher was born in the (real) Dutch town of Leeuwarden in 1898. A poor student at school, Escher was insufficiently qualified to follow his father into the architectural profession and turned instead to the graphic arts. He became obsessive in his pursuit of technical perfection, as evidenced by the controlled lines of woodcuts such as “Morano, Calabria” (1930), or the complex composition of a lithograph, “San Michele dei Frisoni, Rome” (1932), with the Vatican as its backdrop.

Conventional landscapes and city views dominated Escher’s early output, together with two series of folk-art woodcuts, the first made for an emblem book (an antiquated genre in which a symbol is paired with a homespun motto), the second a series of gleeful illustrations to the tale of a mischievous witch, “The Terrible Adventures of Scholastica” (1932).

Then Escher experienced a revelation. The recognizable world of his early works slipped away. In its place came a vision that entirely subordinated the artist’s earlier obsession with technique and representational accuracy.

“There came a moment when it seemed as though scales fell from my eyes. I discovered that technical mastery was no longer my sole aim, for I had become gripped by another desire. . . . Ideas came into my mind quite unrelated to graphic art, notions which so fascinated me that I longed to communicate them to other people. This could not be achieved through words, for these thoughts were not literary ones, but . . . visual images.”

The curators of this well laid out exhibition mark the turning point with Escher’s 1935 “Hand with Reflecting Sphere,” in which the artist holds aloft a gleaming sphere from which his trapped, distorted image peers out at the viewer. It is as if we have passed through the looking glass and stand in the world of Escher’s imagination.

It is a world of visual paradox, as represented by a scattered trio of mindbending works. Earliest and simplest is “Still Life and Street” (1937), in which the flat plane of a tabletop is simultaneously — and seamlessly — the flat plane of a bustling street. “High and Low” (1947) depicts a woman at a balcony and a man sitting on steps below from two different perspectives. The artist’s preliminary sketch reveals that the picture has five different vanishing points!

Similar, but most astonishing, is “Print Gallery” (1957), in which a young man in an art gallery looks at a canvas depicting a harbor town that contains that art gallery in which he stands. This is achieved not by a conventional picture-within-a-picture trick — there is only one picture and only one viewer, who stands simultaneously inside and outside its frame. Escher swirls the composition clockwise and shrinks its scale toward the center. There is a black hole at the heart of the piece, a mathematically impossible space — that is also impossible to draw — sucking in or spewing out this genteel harbor-town world.

Escher was famed for his distortion of space long before Stephen Hawking redrew the universe. A well-known motif in his works is the Mobius strip, a twisted loop that has only one side and only one edge. He also has fun with mathematician Roger Penrose’s “impossible triangle,” a shape that can be drawn but not made — though in “Belvedere” a young man seated in the foreground looks with puzzlement at an “impossible cube,” which he is holding.

But mathematics is only the beginning. Utterly without training in the sciences, Escher seems, in retrospect, to anticipate or explore many fields of modern scientific inquiry. Take evolutionary theory. In “Wonderful Life,” a 1989 study of the Cambrian Era origins of life, the Darwinist paleontologist Stephen Jay Gould speculated as to what might happen if it were possible to “wind the tape of life back” to its beginning, then play it over and over. The chances of natural selection doing the same thing again, producing the same species in the same sequence — including the emergence of homo sapiens — is infinitesimal, Gould concluded.

Escher seems to anticipate this notion in “Metamorphosis II” (1940). This is a long frieze with identical end panels containing the single word “Metamorphose.” The designs of succeeding panels transform and evolve as they approach the center. The initial stages are identical at each end — the word becomes a grid of words, then becomes a black-and-white checker board — then the images take separate evolutionary paths. From the right, the squares form a chess board, then a walled city, a field of cubes, birds in flight; from the left, the squares morph into reptiles, hexagons, a honeycomb, a flight of bees, a shoal of fish. (Fish and birds meet and interlock in the center panel, as in Escher’s better-known “tessellations,” in which unexpected, irregular shapes interlock to make a perfectly flat plane.)

And if Escher plays with evolutionary theories of how we began, perhaps he also shows us what we have become. In a 1980 Pulitzer prizewinning book “Godel, Escher, Bach: An Eternal Golden Braid,” philosopher Douglas Hofstadter speculates that the artist explores the very notion of self. Hofstadter writes in the introduction to the 20th-anniversary edition that Escher’s artwork is central to the “attempt to say how it is that animate beings can come out of inanimate matter. What is a self, and how can self come out of stuff that is selfless as a stone or puddle?”

As groundwork, Hofstadter introduces the (mathematical and artistic) notion of form and ground, whereby one subset is defined by its exclusion from another set. The philosopher illustrates this with Escher’s “Mosaic II” (1957), in which black figures against a white plane define, in the spaces between them, a whole set of other figures (or vice-versa). Others Escher works are similarly used to cast light on Hofstadter’s formulations of artificial intelligence and the nature of consciousness.

Serious stuff. But you don’t need a doctorate in cognitive science or evolutionary biology to understand Escher or appreciate this exhibition. What has made Escher one of the most recognized — and merchandized — of 20th-century artists is his very accessibility, at a time when the sciences seem to be slipping further beyond the grasp of the nonspecialist.

In his own day, Escher lamented the inability of scientists to produce clear explanations of their work. In a letter written to his son, Arthur, on Feb. 15, 1959, the artist writes exasperatedly of a mathematician who found it “very difficult to write intelligibly to a layman.” For himself, Escher continued, “I feel all the more satisfaction from solving a problem like this [the infinite world in an enclosed plane of ‘Smaller and Smaller’ (1956)] in my own bumbling fashion.”

And this, perhaps, is why Escher’s work is so satisfying — it challenges us to figure it all out for ourselves, just as the artist himself did.

For as the early works shown here reveal, Escher’s world — of seemingly impossible castles and fantastical beasts in infinite, interlocking patterns — is actually our world, simply seen through different eyes. The four-dimensional arches of “Other World” (1947) were transported from “Porta Maria dell’Ospidale, Ravello,” which Escher engraved in 1932; the tessellated, imaginary beasts resemble the winged lion that stands in the same city’s square; the concept of tessellation itself was inspired by the tiles of the Alhambra, Spain, which Escher saw in 1922; the insects that crawl and fly through Escher’s multidimensional universes were lovingly detailed in natural-history engravings made in the 1930s.

It’s all around us, comes the realization — if only we learn to look, rather then merely see. “The ideas that are basic to [my works] often bear witness to my amazement and wonder at the laws of nature which operate in the world around us,” Escher wrote. “He who wonders, discovers that this is in itself a wonder.”