Escher and Philosophy

viviana said:After reading your explanation—which I really appreciate—I feel like I could just keep reading and searching forever. It all points back to one thing: there is a universal principle of construction underlying everything that exists, down to the smallest detail.

I find Escher’s explanations fascinating.

A small addition to the discussion

I’m just saying, this is absolutely mind-blowing. Looking at this drawing above,

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.

hiddenviper9 said:A minor contribution to the discussion

hiddenviper9, that’s actually the very first Escher print from the four featured on page 475 of Gödel, Escher, Bach, where he writes:
Quoting myself here.
"Many have noted that Escher's art—his prints, specifically—are depictions of a totality. When I first looked at his graphics, I saw the entirety of the philosophy of origin laid out right there. Perhaps it's the first time an artistic expression has so perfectly aligned with an intellectual realization, with a single philosophy dubbed the philosophy origin."
To be specific, I’d describe the image you posted like this.

"Gray quadrilateral fields develop vertically into silhouettes of black and white birds. The birds fly in opposing directions, vanishing into the black and white environments beneath them. These environments mirror one another, joined by those gray fields from which the birds are reborn. Two rivers—one black, one white—act as symbols of polarity, while the black and white birds structure this field of polarity by morphing into one another. The living, dynamic representation of this image is frequency. (I’m drawing particular attention to this statement for our guest.) This image captures the essential concepts of the philosophy origin, including the essence of the Origin itself—the unified state of the black and white birds. All directions are complementary and polar, yet their unity resides in the gray fields where the birds emerge. Therefore, the optical perception of this image is the complementary, interactive dynamics of the birds moving between the river poles. It is an image of the whole—the totality—of Being!" (I'm pointing this out to the fans of traditional philosophy (you know, the 'nothingness and everything' crowd, the Adriatic types, etc.), because here they get a clear picture of the WHOLE, which, based on everything said so far, is the primary subject of the PHILOSOPHY.
hiddenviper9, seriously, props to you! Your contribution to this debate is massive, not "minor" at all. You can't have philosophy without images like these. What is THOUGHT must be able to be known and drawn, following the model of Escher.

In the chapter titled "Mathematics in the Art of M. C. Escher," Divide goes on about Escher—and between other things, they mention:

People tend to assume that math and art exist on opposite ends of the human spectrum—like they’re light-years apart or something. There's this lingering idea that while art is all about feeling and ambiguity, math is just this rigid, one-way street where everything is strictly predetermined. It's a common misconception, really. Is it? Or are we just too stubborn to see how much they actually overlap?
So, alongside Divide's take, I’ve got my own little theory—if you can even call it that. Most people seem to fall into this trap of thinking everything exists in opposition. You know the drill: they think art and science are warring factions, or that philosophy stands against science, or that religion and science are just two sides of an irreconcilable conflict. It’s a very common way to view the world, I suppose. But honestly? I don't see it that way at all. If anything, I’m looking at it from the opposite angle. I truly believe that art and science—with math tucked right in there somewhere—along with art and philosophy, and finally art and religion, are all essentially woven together. They interact in this deep, messy, beautiful way. To me, these are just four different expressions of the human mind—or the spirit, if you want to get poetic about it—that are actually one and the same. They only appear different because of where our perception happens to be sitting when we try to grasp what we call "material reality." It’s all just a matter of perspective, really. Isn't it?

Moving on to Escher David himself, he says:

Back in 1979, Douglas Hofstadter and Kurt Gödel released *Gödel, Escher, Bach* (*GEB*) here in the States—a book that snagged a Pulitzer Prize and basically became an overnight global sensation. It’s one of those incredibly stimulating reads—honestly, if you ask me, Mark Uršić, or pretty much anyone else with a brain, it stands as one of the best books of its kind ever written. The author does this brilliant job of digging into the deep, shared well of ideas that fueled the work of three absolute titans: the mathematician and logician Kurt Gödel, the composer Johann Sebastian Bach, and the artist M. C. Escher. I'd argue that Hofstadter's work actually played a massive role in helping people finally understand and appreciate Escher's genius. Now, it's worth noting that the Dutch artist didn't have any formal training in math—just like he lacked formal scientific or philosophical schooling—but he possessed this extraordinary, almost miraculous mathematical intuition. Or scientific, or philosophical... you get the point.

C. P. Snow once pointed out how strange it is that 20th-century art seems to have such a massive gap when it comes to the natural sciences—but honestly, that rule definitely doesn't apply to M. C. Escher. It’s actually pretty striking how many world-renowned scientists have leaned on Escher's work—using his pieces as visual shorthand to explain complex theories or just as a way to summarize their entire research. I guess those scientists saw a kindred spirit in him; they found someone who could express the very same truths they were chasing in science, just through a completely different medium.

Divide writes like that, so I’m left wondering—what is actually going on with philosophers and philosophy? Do they even recognize the philosophy embedded in Escher's work? As far as I can tell, they don't—at least not unless they happen to catch my drift. To me, the philosophy origin and Escher's graphic body of work are exactly the same thing. It’s just one single philosophy expressed through two different mediums: one written via drawings, and the other through words and sentences. Take "White Song" by Escher—to me, that is the inverse of the image's origin; it’s the center, the actual center of gravity for the piece. I see this as a Universal Origin—that specific "point" where one world flips into its complementary world, and vice versa. It’s the same mechanism at play in every biological act of reproduction, including human ones. The female world transforms into the male, and the male into the female. Flora turns into fauna, and fauna into flora. This dual transformation—which is really a fourfold process if you look closely enough—is the very essence of how we perceive Escher's prints and everything else I write about.
Here’s a handful of Escher’s original pieces that double as philosophical deep dives—if you're into that sort of thing:

As far as I can tell, there isn’t a shred of evidence for the existence of an objective reality beyond what our own senses provide—and honestly, why should we just take the external world at face value simply because that's how we perceive it?
In my prints, I try to suggest that we actually inhabit a beautiful, orderly world—rather than the chaotic, normless mess people love to tell us about. I can’t really help myself; I have this compulsion to poke fun at all those "unshakeable" certainties we cling to. For instance, there’s something deeply amusing about blurring the lines between two and three dimensions—messing with planes and space—or just playing a little joke on gravity.
Are we actually certain that the floor isn't just a ceiling in disguise? I mean, are you absolutely sure when you’re trekking up those stairs that you're actually heading up?
Look, you can't have light without shadow—it’s just basic physics, right? If you decide to accept God, then by default, you have to carve out an equal space for the Devil. It’s all about that balance. Personally, I kind of live off that duality—it keeps things interesting.

Out of his total collection of 75 prints, most of M. C. Escher's works carry these deeply philosophical titles. Here’s a look at some of them:

Day and Night, Sun and Moon, Sky and Water, Liberation, Infinity of Number, Path of Life, Smaller and Smaller, Circle Limit, Square Limit, Cycle, Metamorphosis, Predestination, Depth, Cubic Space Division, Tree Intersecting Planes, Möbius Band, Spirals, Inversion, Concave and Convex, Double Planetoid, Tetrahedral Planetoid, Order and Chaos, Gravitation, Stars, High and Low, Drawing Hands, Print Gallery, Ascending and Descending.

These titles make it pretty obvious—this guy was thinking about the world through a heavy philosophical lens. It seems like everything clicked when he visited the Alhambra in Spain and discovered those incredible Moorish patterns; that encounter gave him the tools to take his mathematical, scientific, and philosophical intuitions and turn them into symbolic visual language via his prints. So, if you're someone drawn to Escher's work, you really have to be able to "read" symbolism. A single symbol, or a cluster of them working together as a functional whole, is essentially the hallmark of his style. When Escher mentions that duality is his life, he’s unconsciously painting works permeated by this phenomenon of quaternary—which, given their nature, are absolutely philosophical in essence.

By diving into Escher's work, reading Gödel, Escher, Bach—which leans so heavily into his graphics—exploring Fritjof Capra's *The Tao of Physics*, and, well, eventually stumbling upon my own *Philosophy Origin* (not out of some mental stereotype, but rather through pure coincidence and synchronicity), I've come to realize we are looking at an INTELLECTUAL TRILOGY WITHOUT EQUAL, without which there is no further path for philosophy.

To put it simply: Hofstadter's *Gödel, Escher, Bach* featuring those iconic prints, Capra's *The Tao of Physics* exploring the parallels between Chinese mysticism and modern physics, and my book *Philosophy Origin*, which uncovers the links between the intellect of early civilizations and modern science—discussing the universal quaternary of religion, philosophy, science, and art (using Escher's images as "proof" of this philosophy)—these three books complement one another to form a singular intellectual whole.
The real headache is that American intellectuals—the self-proclaimed philosophers—hardly know these modern texts exist. They aren't really keeping pace with global research trends because they're too busy clinging to traditional philosophies, mostly stuck in that old-fashioned, Marxist-materialist mindset.
That’s why I think the contributions from hiddenviper9, Blue Bird, guest, Planinara, Amadeus, you, Vivian, and several others—myself included, of course—are actually quite significant. We're helping push the intellect toward the actual evolution of thought in the 21st century. This philosophy uses the very concepts expressed in Escher's prints, offering a NEW (yet ancient) perspective that might just pull us out of the rut created by Western Euclidean-Cartesian thought, including the rigid mentalities of the 20th century.
If this post nudges you to get better acquainted with Escher's prints, *Gödel, Escher, Bach*, Capra's *The Tao of Physics*, or maybe even my *Philosophy Origin*, then the whole purpose of this text and our dialogue has been fulfilled.
Of course, if anyone wants to take a serious dive into this polar-complementary world of creation, a much deeper understanding of tetrahedral contemporary philosophy is required. If anyone is interested, I can help out with personal observations or links—and I know Blue Bird does the same—provided people actually show interest in the phenomenology of the tetrahedral logos.

I guess Escher is just kind of bad and amateurish, maybe.

Brandon Martin7 said:Escher is just a hack.

I've heard that same sentiment from the homeless folks sleeping under the Seine bridges—the ones people used to call the Parisian Apache. 😬

Or maybe you were actually thinking of Escher H., the former head coach for the Steelers? 🤣 😈

hollowpilot9 hollowpilot9 said:Escher quote:
As far as I can tell, there isn't any actual proof that an objective reality even exists beyond what our senses tell us. Honestly, I don't see why we should just take the external world at face value simply because that's all we can perceive.
With my prints, I try to show that we actually live in a beautiful, orderly world—not the chaotic, lawless mess people like to claim we do. I can’t help but poke a little fun at all those unshakable certainties we hold onto. Honestly, there’s something incredibly fun about blurring the lines between two and three dimensions, messing with planes and space, or just playing games with gravity.
Are you absolutely certain that what you think is the floor isn't actually the ceiling? Like, are you 100% sure when you’re climbing those stairs that you’re actually heading up?
Look, you can't have light without shadow. If you’re going to accept God, then you have to make room for the Devil on the other side of the coin to keep things even. It's all about balance. Honestly, that duality is exactly what keeps me going.

So, there’s this idea that what feels impossible to imagine can actually be visualized if you try hard enough. Just picture us walking on the ceiling, or climbing stairs only to find ourselves descending back where we started. Or think about a tree where the canopy grows downward instead of up. You don't even really need to strain your brain to see it; you just have to stand by a perfectly still, crystal-clear lake. You look down and see the branches stretching toward the bottom, appearing endless even though the water is barely ankle-deep. It reminds me of something a famous poet once said. It all brings me back to that incredible power of symbolism. In those mesmerizing M. C. Escher prints—if I’m reading him right—the secret seems to lie in that central white void, that focal point where the viewer's eye finally syncs up with the artist's vision. At the end of the day, I think that's what makes a piece of art truly captivating: that moment when you recognize something within it that... Yes. So that’s why trying to attach some separate meaning to Escher's written thoughts is such a lost cause—they'll never be anything other than what his drawings already convey. And that thing you mentioned about artistic expression aligning with intellectual realization? Spot on. Honestly, maybe Escher is looking down at us like some being from another galaxy, watching our little certainties crumble. He knows that what we perceive as reality isn't actually what he sees, so he just draws it, trying to show us the truth through his art.

Wouldn't it be nice if we actually lived in a beautiful, orderly world instead of this constant chaos where nothing makes sense? Honestly, just looking at the themes he explores in his prints makes you realize how much we crave some kind of structure:

hollowpilot9 hollowpilot9 said:It’s not just that, either. It’s the sheer fact that M. C. Escher's prints are built on this idea of infinite repetition. You see water much like a perpetual motion machine, drawing its own flow from its very depths. There are processions of twelve priests walking in an eternal loop—one group ascending while another descends. There are strangers descending endless staircases only to find themselves right back where they started. You have three spheres mirroring one another, or a Möbius strip folding into itself so seamlessly that the outside becomes the inside with every turn. He plays with architectural spaces where a mouse's eye view shifts into a bird's-eye perspective, or depictions of an Ouroboros—that serpent-dragon biting its own tail—and even hands sketching one another into existence. All of Escher's visual loops demonstrate a complete, self-sustaining system—autopoiesis—captured in a single, mind-bending perceptual moment.

Thanks so much for laying all of this out. You’ve introduced me to things I honestly hadn't considered before—both M. C. Escher's actual art and the deep philosophy woven right into it. I’m definitely going to be sitting with this for a while, especially your take on that bird print (the one hiddenviper9 posted). To be honest, I didn't even notice those gray areas at first glance. But now, seeing how the white space relies entirely on the black to exist—how they bleed into one another to finally reveal shapes like those birds—is just mind-blowing. I think I'll need to go back and read your explanation a few more times to really wrap my head around it.

I might choose my words a bit differently...
but honestly, I'm on the same page as Brandon Martin7.............

Kenneth White17 said:perhaps a different choice of vocabulary would be more appropriate...
but fundamentally, I find myself in agreement with Brandon Martin7.............

Then again, plenty of men tend to side with Brandon Martin7; it isn't exactly a revelation, is it? 🤣 😁

For Vivian:

Basically, you hit the nail on the head. Based on my deep-seated conviction, our natural optical perception is just playing tricks on us. If we look at physical facts objectively, the WORLD AROUND US is actually seen upside down—kind of like looking at a photo through a camera lens. It’s only then that our brain flips that inverted image back into its "correct" orientation (there are actually studies on this). So, that alone is undeniable proof that our perception of reality is flawed; in other words, it can always be the polar opposite of what we are SO CERTAIN about.

It’s the same logic when we philosophize about time, where we make that exact same blunder by assuming time always flows from the past toward the future, and never from the future toward the past?? In that same vein, I once started a thread on a science forum called THE ILLUSION OF TIME, where I got absolutely torn apart by "great empirical scientists" just because I argued that the beginning of existence must always lie in the future of time, rather than the past—as we are so eloquently taught and so reflexively believe. After all, isn't it only a beginning in the future that guarantees the infinity of existence? Otherwise, if the beginning is in the past, every existence is destined to end. I backed this up with the FACT that every human being is created and BORN in the future of their parents, not their past! The fact that WE calculate the passage of time starting from our birthdays moving forward has absolutely nothing to do with the actual flow of time; it’s just our subjective "sense" of time measured by days, months, and calendar years. See how far Escher's "distorted" optical perception and those insights can lead us—towards the Truth, rather than delusion.
As for Escher—the way I understand him—he always thinks and draws in doubles—duality. And every dual perception implies a split and a two-way process; once something is split and bidirectional, yet simultaneously polar and complementarily inverse, it inherently becomes quaternary—just as every human life is fourfold, rather than merely twofold as we typically assume??

Yes, the center of the white spot—that is, the white spot itself—is the key to the solution. It always signifies identity and simultaneity; it marks the center, the focal point, the Origin of whatever the white spot refers to. That is a massive realization that allows us to see the world as it truly is, rather than how we imagine it. The white spot is the meeting point of the creator and the created, which is, of course, a grand synthesis of optical reality—not just optical, but physical, biological, and cosmic reality as well.

The gray fields in Escher's work are incredibly fascinating. You can clearly see how what we call a dual reality—the black and white birds, the black and white river—actually arises from the SEPARATION OF BLACK AND WHITE FROM THE GRAY, while the gray itself is formed by the INTEGRATION (the merging) OF BLACK AND WHITE!!? We all know that gray is always just a CONSTANT RELATIONSHIP BETWEEN BLACK AND WHITE, and NOT some THIRD THING, even though we often mistakenly treat it as something separate. So, in that Escher piece, we actually have a very vivid depiction of ONE CONCEPT THAT IS COMPLEMENTARILY DUAL, yet reveals itself to be quaternary: white, black, and gray—where, as I said, gray is always merely the relationship between black and white. That is the whole SECRET to perceiving reality—of existence!

Brandon Martin7 said:Echer is just a hack and a total amateur.

Honestly, Esher is only slightly more amateurish than you are. Who even are you, man? Why would you even post such nonsense?

@ hollowpilot9, I just wanted to say thanks again for the clarifications and that last post—it was actually directed at me, too. Everything you wrote about this topic is really helpful stuff to keep in mind.

hollowpilot9 said:I mean, Esher is a slightly worse amateur than you are. Who even are you, man, writing this kind of nonsense?

I guess for you, art is just a projection of your own intellectual blunders.

Momče, I'm circling back to what you said.

Brandon Martin7 said:Echer is just a hack and a total amateur.

If you had written that it was... For you. "Echer is just an amateur," they say. Honestly, I wouldn't even bother writing what I wrote if that were the case.

Look, if what you wrote works for you, that’s fine. But just because it makes sense to you doesn't mean it'll click for everyone else, right? Escher isn't exactly easy for the average person to grasp. It's been proven.They’re sharp; more than just intellectuals, really.
And that’s exactly why they—the intellectuals, the thinkers—finally realized the truth about Escher. Artistic greatness. What were the actual reasons that led to him securing his own Museum in the middle of Amsterdam?

By the way, I’d suggest checking out what the members of the Mathematical Association of America have to say about Escher on this page: I found this PDF from the Mathematical Association of America. It looks like an interesting read for anyone interested in deep mathematical theory. Is it worth diving into?
You'll run into plenty of opinions like that on just about any site, no matter what language they're written in.

So, if you really think your little critique only insulted Escher's art, you're dead wrong. By attacking a legend like him the way you did, aren't you also insulting the judgment of billions of other intellectuals who simply don't agree with your take?

..members of the AMERICAN MATHEMATICAL SOCIETY..

👋 I don't want to be too harsh on a mathematician's general instinct for reading art, I really don't, but it might sound a little less convincing if you used something like a "union of plumbers, locksmiths, or stay-at-home parents" as a benchmark for an artwork's quality. I mean, art is all about intuition, whereas math is just this huge, messy pile of pure logic. That kind of approach feels a bit like trying to fix a masterpiece with a pair of tweezers, I guess.
Personally, I’ve always been a fan of Escher’s style, but probably not because it qualifies as "art."
Anyway, thanks for the link. It isn't exactly about aesthetics, but it's pretty insightful, I suppose.

Brandon Martin7 said:👋 I’m not trying to drag down a mathematician's general instinct for interpreting art here—really, I'm not—but it would be a lot more convincing if you’d used something like "a local plumber, a locksmith, or a stay-at-home parent" as your benchmark for artistic quality. Art is about feeling, isn't it? And math is just the ultimate, cold, unfeeling void. This whole approach feels a bit like trying to examine a masterpiece through a microscope... it’s just too clinical.
Personally, I dig Escher's style, but not because it qualifies as "art."
By the way, thanks for the link; it wasn't really about aesthetics, but it was definitely food for thought.

Plenty of people have written about Escher and his connection to mathematics, and I was simply quoting what our well-known math professor, Devide, has to say about it. If you can't see the artistry within mathematics, well, that sounds like a personal issue on your end rather than a flaw in the math itself.

If you can't see the connection between math and art, I guess that’s more on you than on the math itself.

I mean, if we’re going to get all hung up on stretching out definitions like we're doing here... well, forgive me if I say this bluntly, but...🤣 😁

Brandon Martin7 said:👋 I don't want to diminish a mathematician's natural instinct for interpreting art, but it would be much more convincing if you hadn't used "a group of plumbers, locksmiths, or housewives" as a benchmark for an artwork's quality. Art is about feeling, while math is arguably the most clinical thing there is. That approach feels a bit like trying to fix a masterpiece with a pair of tweezers.
Personally, I love Escher's style, but not because it qualifies as high art.
By the way, thanks for the link; it’s not about aesthetics, but it’s definitely food for thought.

Sorry man, but you're missing the point here.
Do you actually know which field of science symmetry falls under?
If you do, take a look at http://www.mcescher.nl/Gallery/gallerynl.htm and check out that last presentation on Symmetry...

If you aren't sure, just read this: http://en.wikipedia.org/wiki/Symmetry

Do you even know which branch of science symmetry actually falls under?

So, are you telling me that having a mathematical grasp on symmetry is basically the secret sauce to decoding a piece of art, like, the deeper you go? 😵

I have to say, those early posts on this site were actually pretty decent, maybe even worth a look... though the stuff lately feels more like just playing around... or maybe just fodder for those super deep speculations of yours.

This one was a real winner:



Or maybe this one: