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hollowpilot9 said:For Vivian and anyone else curious about Escher:
I promised I’d share some thoughts from people who actually recognize Escher's mathematical, philosophical, and scientific genius—rather than just seeing him as some "ordinary" graphic artist who "has no clue" about math, philosophy, or science. Is it really that hard to see the connection?
It all starts with Hofstadter's book Gödel, Escher, Bach, where those three letters stand for Kurt Gödel, Escher, and Johann Sebastian Bach. But we're focusing strictly on Escher here, and the story begins like this:
I have an essay by Mark Uršić titled "Homo ex machina? — or — The Boundaries of Isomorphism," where he writes:
"The first time I encountered the book Gödel, Escher, Bach, it happened to fall open to page 714, where I caught sight of an unusual print titled 'Print Gallery' by M. C. Escher. Through its hyperrealism—which, in a sort of self-referential loop, twists itself into extreme surrealism—the piece completes a circle."
After this transformation, Uršić notes, "My eye, the observer's eye, plays tricks on me, mimicking the author's; so it isn't surprising that Escher tucked his tiny, barely visible signature—his very name—into that central white spot."
"Flipping through Gödel, Escher, Bach, we encounter a canon that grows infinitely: Achilles and the tortoise, artificial intelligence, the reflection of a celestial city in a vast ocean, theorems of propositional calculus, the Tower of Babel, non-Euclidean geometry, the Cretan labyrinth, Fibonacci's numbers, ideal crystals in a magnetic field, hieroglyphs, Bach's crab canon, Zen Buddhism, termites on a Möbius strip, tornadoes and quarks, the structural over-determination of ant colony consciousness, brain neurons, Gödel's numbers, the myoglobin schema, Turing's set, a verse from the Quran, Magritte's pipe, computer programs, the recording of a proud fugue... and so on, indefinitely. What do all these worlds have in common—aside from that white spot in the middle of the circle?"
Who would ever guess that "the isomorphism of Bach's canon has anything to do with Escher's 'Print Gallery'"? And it doesn't stop there. Escher's prints constantly depict continuous repetition: a waterfall that acts like a perpetual motion machine, drawing water from its own depths; a procession of twelve priests walking eternally in a circle, some upward and others downward; strangers descending endless stairs only to find themselves back at the start; three spheres mirroring one another; a Möbius strip twisting into itself so that the outside becomes the inside at every turn; architectural spaces where the perspective shifts from mouse-eye to bird's-eye view; an Ouroboros—the snake-dragon biting its own tail; hands drawing other hands, and so on. All of Escher's graphic loops demonstrate a complete, self-sustaining autopoiesis within a single perceptual act."
And so, Escher—the graphic artist—takes the previously disconnected threads of art and math, art and philosophy, and art and science, and uses them to gently introduce Western philosophy into a world of complementarity, polarity, self-creation, and self-contradiction. It’s enough to drive not just the viewers of Escher's work mad, but anyone trying to assign a different meaning to these written thoughts than the ones captured in Escher's drawn thoughts.
To really dive into the implications of Escher's art, my next post will feature excerpts from Vladimir Divide's book "MATHEMATICAL READER," which I bought for a few "pocket change" bucks $3.00, which honestly just goes to show the current level of intellectual depth and academic interest here in the States.
I mean... I'm really just out here splitting hairs at this point.
Look, colleague—mathematics and art have been intertwined since the days of ancient Egypt, yet we still haven't even managed to translate their six foundational scrolls on the subject. People love to talk about the "inseparable connection between art and math," as if it’s some new discovery. It isn't. Three hundred years before M.C. Escher started playing with perception, Leonardo actually pulled off the impossible—fitting the human form perfectly within both a circle and a square. You might call it pure geometry, but that's a simplification—there is an immense amount of complex ratio work and calculation involved behind the scenes. And let's not even get started on the thinkers who came before him; they understood the golden ratio intimately, documenting it extensively in countless treatises long before it became a modern obsession.
The golden ratio isn't some mystical phenomenon—it’s nothing more than a double ratio, pure and simple mathematics. We see traces of it stretching all the way back to ancient Egypt, though I honestly have my doubts about whether those builders actually understood what they were doing. Did they truly grasp this concept of a "divine proportion," or was it handed to them by some higher power? Or, perhaps more likely, did they just stumble upon it through basic aesthetic intuition long before anyone officially "discovered" it? It's much more plausible that they simply gravitated toward it because it looks right, rather than following some complex formula they couldn't possibly have known.
It’s a bit of a misconception that Western artists just stumbled upon the golden ratio out of thin air—they actually earned their stripes by digging through the archives of ancient civilizations, specifically those foundational works coming out of Greece. We're talking about deep dives into texts like those ten volumes on temple architecture penned by Marcus Vitruvius Pollio. It wasn't magic; it was rigorous study.
(The 1st century B.C.!!!!)Leonardo's "Vitruvian Man"—the one that gave the whole concept its name—essentially breaks down how mathematics can be applied directly to the arts, specifically within architecture. It’s all about that golden ratio; using pure numbers to dictate the physical structure of our world.
Look, your post is fine, I suppose—but there’s something undeniably off about it. You spend so much time quoting others only to pivot into a few sentences that just... explode with sensationalism. It’s jarring. Honestly, if you’re looking to lean that hard into the drama, maybe you should have considered a career in journalism or politics instead. Now, don't get me wrong—M.C. Escher's work is absolutely fascinating, but...
It’s like this—it serves as a narrow gateway into Western philosophy, dragging us into a world defined by complementarity, polarity, self-creation, and those deep-seated self-contradictions that don't just drive viewers of M.C. Escher's prints mad—they also mess with anyone attempting to find a different kind of meaning in written thought than what is already visually etched into Escher's designs.
Why through small doors ???
He isn't even touching on that kind of stuff—you know, all that nonsense about complementarity, polarity, self-actualization, or those self-contradicting tropes—which is frankly just trash. Absolute garbage. But, I will say this: his imagery is incredibly compelling.
"It drives illustrators crazy"—what?! Look, that only happens when you're sketching out technical diagrams and accidentally misconnect a few nodes... maybe those kinds of images used to mess with people's heads back in the 19th century—or even earlier—but honestly, I don't think they have that kind of effect on anyone today.
Look, like I was saying before—and I’ll stand by this—there is just far too much sensationalism being thrown around here for what is essentially an analysis of a single painting style. It's excessive.
Look, I’m genuinely glad to see the younger generation still taking an interest in art and philosophy—truly, I am—but this shallow, sensationalist approach to everything? It achieves absolutely nothing. It’s all flash and no substance, which I suppose might fly with the crowd that spends their weekends obsessed with *The Bachelor* or some other mindless reality TV trash, but let's be honest: it’s just idiocy reaching new heights. That said, I will give credit where it's due—I respect the effort being put in.
Hey there. Hope everyone's doing alright.
P.S. "If someone has already weighed in on this—well, I clearly missed it."