In Princess Tutu, anybody who isn't directly connected to the story sees the eponymous Magical Girl as a giant white swan wearing a crown.
Death Note's 13th volume, How To Read, mentions that the true form of the Shinigami King is unknown and may be incomprehensible to humans.
Baccano's Ronnie Suchiart reveals his true form in the light novels once. No physical description is given, however, on the basis that the sight was so terrifying and incomprehensible that it was blocked immediately and entirely from the spectator's memory.
Implied regarding goddesses and demons Ah! My Goddess; because they exist in a twelve-dimensional state naturally, four-dimensional beings such as humans cannot truly perceive them. This was most openly stated in chapter 268 where a demon purposefully forced Keiichi to witness a bit of her true form and nearly shattered his mind.
Mokkurkalfi: You don't perceive our true appearance. Your existence and ours are different. My form, and what you think you are seeing, are not necessarily the same.
Several characters in A Certain Magical Index have "unexplainable" abilities. Ollerus (a ridiculously powerful sorcerer) and Gunha Sogiita (Level 5 esper) are a couple... Gunha doesn't even know how his own abilities work (he thought he figured it out at one point, but was told that he was wrong). This is actually a great boon to these characters, as if your opponent doesn't understand what they're being attacked with, they cannot form an effective defense against it.
The enigmatic being Aiwass. When Accelerator gets his ass kicked by it, Accelerator has a difficult time comprehending what his foe was.
A Majin wields power that very few can understand. When Othinus (a true Majin) and Ollerus (a "failed" Majin) have a brief battle, bystanders can tell that something happened between them, but they cannot explain what.
Comic Books
It's often said that Galactus doesn't actually look like a gigantic human - it's just your brain that makes it that.
Turns out he was a Human Alien in the previous universe before he became Galactus, but now his true form resembles a star.
In one instance◊ when Galactus appears before a large number of species, the page is filled with numerous smaller pictures showing how each species perceives him. Some of them does look pretty horrifying.
In the JLA/Avengers crossover: after flying into space, Superman and Iron Man see the forcible merger of their worlds as two gigantic hands pushing the two Earths together. Tony comments that this can't be real, and Clark says that this is simply how their minds chose to represent the event.
Left behind in the space where the "merger" took place is an egg that will explicitly become the center of a new universe someday. Make of this what you will. (At any rate, it certainly gives Big Bang a whole new meaning.)
In an early Justice League of America comic, the JLA encountered a monster calling itself The Unimaginable, a creature so far beyond human comprehension that it was effectively invisible.
Toyed with in the tale of Orpheus in the Sandman Special, reprinted in Fables And Reflections. Orpheus visits Death and becomes confused and disoriented when he sees her in her house clothes. She quickly cleans up for her visitor.
Due to miscommunication at DC, the death of the New Gods in The Death Of The New Gods were completely contradicted by the death of the New Gods in Countdown to Final Crisis. Grant Morrison says they both happened, and are merely different mortal viewpoints of an event completely beyond our grasp.
In the Superman story Whatever Happened to The Man of Tomorrow?, Lois Lane tries to tell what Mr. Mxyzptlk's true fifth-dimensional form was: "I can’t describe what Mxyzptlk then became. He had height, width, depth, and a couple of other things, too.”
The Vishanti, a trio of higher entities who sponsor the office of Sorcerer Supreme, explicitly state that they cannot show their true forms to mortals because it would wreck their minds.
In Guardians of the Galaxy, it's explained that forces and entities, like the Abstracts, sometimes simplify themselves for mortals in order to get their assistance. In the some issue, it's revealed that the setting, what looks like a giant checkerboard-like world, was actually the cloak of a gigantic Abstract.
In Harry Potter and the Methods of Rationality, Dementors are this... unless your conscious mind can solve the riddle they represent, in which case you do see the true form.
In the Pony POV Series, the Elders of the Alicorns and Draconnequi are Eldritch Abominations (though the Alicorns are benevolent), and as such cannot be properly viewed by mortals. This is best exemplified when Liarjack meets the Father of Alicorns — the only thing she's able to view him as is a piece of the Night Sky in the shape of a pony (probably due to him being the Anthropomorphic Personification of existence). Everything else about him is so seemingly contradictory (such as appearing as a foal, a colt, and a stallion all at once), she's incapable of understanding it, and finally just gives up trying to in frustration.
Film
In Dogma, God manifests twice in A Form You Are Comfortable With (most famously as Alanis Morissette), but His/Her voice is a perfect example. Humans' heads and chests explode upon hearing it because we do not have the aural capacity to handle its awesome power, which is why God usually sends an Angel to communicate with humans.
The Metatron: We went through five Adams before we figured that one out.
No one knows what the true (or original, if you prefer) form of The Thing (1982) is. Not in John Carpenter's version, anyway.
This is one of those subjects that "one could go crazy thinking about" as Carpenter put it in the DVD commentary. And it remains debated by the fans.
John: I think we can assume that these entities are more advanced than us. Why don't they just come right out and tell us what's on their minds?
Leek:You're more advanced than a cockroach. Have you ever tried explaining yourself to one of them?
It is said in the Devil that the devil can take on any form and gender.
Sauna in the movie Sauna appears to humans as sauna, while it really is something more. This is most likely because it chooses to appear in a form that people can comprehend.
The angels in His Dark Materials are described as being like this - humans and even witches see them as human shaped, being incapable of perceiving their true form which is more like architecture. At least until Baruch and Balthamos come along and really do seem like nothing more than slightly snobby see-through humans.
The monsterIt from Stephen King's book of the same name. The closest approximation for its physical form that the protagonists could comprehend was a Giant Spider.
This also happened with the eponymous character of Stephen King's novel Rose Madder, whose true form was something like a spider... thing. Rosie was warned several times not to look at it.
This is a regular feature on Discworld, particularly as it relates to death (and indeed Death!) It's also how the Time Travel antics of the Men In Saffron appear to civilians.
Death gets this whenever he interacts with humans, who seem confused because someone is talking to them, and it appears to be a skeleton in a cloak, but that's ridiculous, so the mind just rejects it. Children, however, aren't nearly as mentally fixed, so their minds easily wrap around it and they see him as he really is.
And there are occasions when Death CAN be seen. Most notably, in Wyrd Sisters, when Death decides to take the place of an actor who is supposed to play him in a Macbeth expy, everyone in the audience is expecting to see death and, therefore, does. Death, not being used to such a large audience, gets stage fright. And it is hilarious.
Non-magic users, not having octagons in their eyes in addition to rods and cones, cannot see octarine, the eighth colour; instead, they only see blackness.
Mostly averted in H. P. Lovecraft's works as his Eldritch Abominations tend to appear in their true form, which tends to lead to madness in those who see them. Sometimes it's played straight, though:
Yog-Sothoth is perceived by mortals as congeries of iridescent spheres because his true body transcends the space-time continuum and we only see the small parts of it that happen to intersect with that particular location in time and space.
Nyarlathotep tends to appear in a form of a man because it makes manipulating humans easier. He has several less human forms too (1000 to be exact) but all of these are just avatars, or "masks". What his true form looks like is never even hinted, but as he is the soul of the Outer Gods, he might not even have a physical body outside the avatars.
Although it's never explicitly mentioned, considering the insignificance of mankind in Lovecraft's cosmology it's very unlikely that the Elder Gods naturally look humanoid. More likely the human-like forms they appear in are used by them in order to not drive humans insane. The Elder Gods oppose the Great Old Ones, and since mankind would be destroyed if the Old Ones awaken, they are the closest thing the Derleth-subscribed mythos has for benevolent deities. Not that that's saying much.
In Through the Gates of the Sliver Key, Yog-Sothoth explicates a major implicit premise behind the whole Cthulhu Mythos: practically everything we experience goes under this trope, including three-dimensional space, change and time, and the individuality of what we ordinarily think of as different creatures. Ramsey Campbell's "The Render Of Veils" exploits this variation of the trope to very disturbing effect.
In the Otherland series by Tad Williams, Felix Jongleur communicates with The Other through simulations so he can avoid interacting with it more directly. Unusual in that he's the one who determines what fake form he's perceiving, though The Other tends to warp the simulation into something a bit more disturbing.
The NA Sky Pirates! features a small pocket universe that is one of these, which is hiding a totally separate species that is also one, and it also heavily implies the Doctor himself falls into this category. Its loose sequel Death and Diplomacy extends this to the TARDIS too.
The Ellimist always appears in a humanoid form before the Animorphs, while his true form is some techno-organic behemoth made out of countless pods, organs, feathers and the like, built around his original avian body, about half of which is still trapped inside a black hole.
Angels are like this in C. S. Lewis' Space Trilogy. Most of the time they just look like a vague shimmer of light; other attempts have produced wheels rolling on distant hills, a painful impact of colors (described as being like the "true sensation" of being hit in the eye by a rock), and (most successfully) a pair of otherworldly humanoids.
There is a scifi short story about a creature that is not of alien form but of alien color rendering it impossible to see properly.
Sounds like "The Colour Out Of Space", one of H. P. Lovecraft's more famous works.
Could also be Ambrose Bierce's "The Damned Thing".
In Larry Niven's Known Space series, Hyperspace has this quality: the human brain is completely incapable of perceiving hyperspace, and carefully edits it out of your sight. If you look at a window, you see the frame basically collapsed all around the window, which is slightly less disturbing. And if you look at a 360 degree panorama or hyperspace, you lose sight completely: you don't just go temporarily blind, your completely forget that you ever possessed sight, or what sight even is.
This is for the lucky, space-worthy people. About 60% of humans simply go stark raving insane the moment they clap eyes on hyperspace. Passenger liners don't have windows at all, because they don't want to destroy the passengers' minds.
And the space-worthy people have to deal with the fact that the "Blind Spot", the parts your brain edits out, will eventually start growing. First your brain just refuses to see the window, but eventually everything nearby will be "pulled in" as your brain desperately tries to edit out things that start being associated with the Blind Spot's location; you stop seeing the entire wall, then the walls connected to that wall, then...
A particularly nasty variation happens in Harry Potter, in the Boggart that takes the form of whatever you happen to fear most.
Also happened over a decade before in the Worlds Of Power novelization of Blaster Master, in which the Big Bad takes the form of whatever each person fears.
In The Dresden Files, there is a semi-divine being known as a Skinwalker, or Naagloshii. Just to look at it resembles a powerful bestial creature (with the ability to shape-shift). Certainly frightening, but by no means incomprehensible. However, when Harry uses his Wizard's Sight on it, even briefly, the effect is almost mind-shattering. The Naagloshii's true form is so inherently wrong that it literally takes hours for Harry to dissemble enough to function normally again (and he has to be careful not to think about it otherwise it reduces him to near unconsciousness).
It is implied that the powerful movers and shakers of the supernatural world have similar (if not so utterly abominable forms). The Queens of the Sidhe, particularly Mothers Summer and Winter, are beings of such intrinsic power that their true forms are likely to be completely incomprehensible.
He Who Walks Behind is so alien that even his name cannot be comprehended, merely experienced as a rush of ugly emotions and a deep-seated hatred for all mortal life.
Played straight and subverted in Dan Abnett's Know No Fear. While fleeing from Chaos Daemons two Guardsmen perceive them as horrific monsters with horns, spikes and forked tongues. However one member of their party, the seemingly immortal Oll Persson thinks to himself that what they are seeing is not the true form of a Daemon, it is what their minds are perceiving it as by pulling together bits of what they believe monsters look like. He however sees their true forms as shapeless clouds of warp energy and is able to kill them.
The various dieties in The Elenium and it's sequel series The Tamuli are hinted to be this, seeing as Aphrael can appear as a child, a grown woman, and even two people at the same time.
In E. E. "Doc" Smith's Lensman series, it is impossible for anyone to properly see a Palainian or any other being that lives in distant planets that are perpetually cold. This is because these beings survive by being four-dimensional (this is described as a "hyper" dimension); since everyone else lives and perceives in three dimensions, this extra-dimensional aspect is lost on them.
Live-Action TV
In Babylon 5, most people see the Vorlons as whatever equivalent their culture has to "angel," but Londo apparently sees nothing. Whether this was because the Vorlon ignored the Centauri race and focused their ancient genetic manipulation on the now-extinct Xon race that also evolved on Centauri Prime, or because Londo is just a Jerkass, is never explained.
JMS claimed somewhere, in response to a fan's question, that Garibaldi (an agnostic) would have seen himself in Kosh. This statement seems to support the idea that it was Londo's having been touched by Shadows that led him to see nothing, rather than any faith-related matters/crises on his part.
Parodied somewhat in The Middleman, when MM and Wendy visit the underworld. It appears to Wendy (and the camera) like an office building, but when she mentions this to MM, he claims to see an overgrown field full of feral creatures. He's kidding, he sees an office. "Someone's funny in the underworld."
Many portrayals of the Q Continuum, including the episode "Death Wish" of Star Trek: Voyager, indicate that whenever a human enters the Continuum it looks like normal 4D space-time so that the human mind can comprehend it. In that episode, the crew joins the Q Continuum rebels against the Q old guard. Because the humans (and aliens) cannot comprehend Q weapons, they perceive the situation as the American Civil War... even the weapons they're using against the old guard Q. (Tuvok threatens these Q with their own weapons after being insulted.)
The novel I, Q goes so far as to say that the human mind does this automatically to stay sane and that Data normally shuts down because his android mind tries to "see" everything and crashes. Q must filter the sensor input so Data can function.
In fact, the Q Continuum has never been truly perceived by visitors; they're always shown a representation which they could understand.
In one novel, Picard perceives the Continuum as a weird-looking highway with a sign at the on-ramp saying something like "Organians, keep out!"
The book also mentions that the Q don't like the Organians for their smugness and the holier-than-thou attitude. Which is like a teapot calling a kettle black. Is there anyone in the galaxy more smug and self-righteous than Q?
In Supernatural, angels cannot be comprehended except by their true vessel. Anyone else who glimpses their true form has their eyes melted out of their head, and anyone else (or anything around anyone else) that is around their true voice experiences what basically amounts to tornado conditions. To even be comprehended, they must first take a vessel. Any improper vessel, even the next closest thing, will eventually explode under the power.
Archangels are even worse. The very presence of their true form is capable of doing all of the above, but with massive earthquakes, and instant death for anyone who's around.
And this can even remain true when they're in a vessel. Raphael simply manifesting himself created a thunderstorm that knocked out all power to the Eastern Seaboard. In a later episode, he similarly created another thunderstorm when he manifested again. And when he showed up to protect a prophet, the growing light was tearing the room apart.
According to Zachariah, his true form has 6 wings and 4 faces, one of which is a lion. This is actually in line with how The Bible describes angels.
In Grimm, it's explained that it's generally a bad idea for normal humans to see the true forms of Wesen, as it could make them Go Mad from the Revelation. Someone like Hank whose sanity was able to withstand the initial shock then thinks he was going crazy. For weeks, he was unable to sleep and was becoming increasingly paranoid. Nick had to stop him from shooting his own goddaughter in a blind panic when she accidentally reveals her Game Face.
The Weeping Angels from Doctor Who, maybe. They can't be seen by any living being, and any time they can be observed, they instantly freeze into their trademark stone statue forms. It's implied, however, that they aren't necessarily limited to the form of angels when frozen in stone. We don't know why they freeze into rock beyond it being a defense mechanism, but for this very reason, what they are/look like unfrozen is anyone's guess.
Observer in Mystery Science Theater 3000 insists that he exists only as a brain, and that if "lesser minds" perceive a body carrying around said brain, it is merely this trope in action. (All evidence in the show suggests that yes, he does have a body, although his brain is indeed outside of it.)
Religion & Mythology
The Bible, in the Old Testament, God has mentioned that if anyone unprepared saw His face, they would die (read: annihiliated). Even Moses, his most obedient follower, could only see His back. God, like Yog-Sothoth, also is omnipresent and exists at every point in the space-time continuum simultaneously yet transcending all of it, and Jesus is just A Form You Are Comfortable With. Islam takes this bit particularly seriously; arguing that if God's true form is alien and utterly incomprehensible to humans, then you cannot picture Him as anthropomorphic, therefore doing so and worshipping God through pictures is considered blasphemous, heretical idolatry (Christianity under the Byzantine Empire also tried this but failed).
Which then rubbed off on Moses a bit, since when he came back to everybody else his face blinded them into making him wear a veil.
All which is rather odd, since Abraham had no trouble with having God visit his tent and chat with him, face to face.
Notably, this is somewhat subverted in the Catholic faith, as the saints will get to see God in all his glory in Heaven, often referred to as Beatific Vision. The idea behind it is that it should destroy your very soul, but God, being God, could perserve someone from letting tat happen.
Also applies to the Seraphs, God's personal throne guards. They keep themselves hidden with their wings (they have six or more, by the way), as any mortal who looks at them directly bursts into flames or get annihilated instantly.
All this stuff is technically moot if you think about it, since you only get to meet God and the seraphs after you're already dead and in Heaven.
Speaking of Heaven, some believers reject a Fluffy Cloud Heaven and Fire and Brimstone Hell interpretation of the afterlife, instead preferring a metaphor-based no-true-form spin on where we cannot really comprehend the true form of those dimensions, and the literal interpretations above are just approximate interpretations of what is really happening in there. For example, Heaven is a state that is expressed in metaphor as a place of peace and bliss, while Hell is filled with so much of all kinds of sin, chaos, insanity and perversions against nature that the human (and supernatural) mind is unable to cope with it, and tries to resolve it into a Hell it can comprehend and express in art, namely a dark inferno filled with pain and disgusting Eldritch Abominations.
Averted with Jesus generally, although revealing Himself to Paul later on (after the Ascension), is likened to a lightning strike and knocks Paul off his horse, temporarily blinding him.
Some forms of Gnosticism play this straighter, teaching that Jesus never was physically incarnated, and had no tangible form.
The New Testament condenses all of its incomprehensibility in the book of Revelation. Okay, so the four horsemen and great seven-headed beast are all probably metaphorical... and maybe angels in their native environment really are humanoids, some with six wings and using four of them to cover their faces and feet, or have four wings and four faces... but then John talks about things like how "the sky rolled up like a scroll," and you start to get an inkling of how everything this poor man's mind was experiencing utterly defied all human comprehension.
Older Than Feudalism: In the Bhagavad Gita, Krishna actually shows Arjuna his (God's) true form, which is basically a more extreme combination of Eldritch Abomination and Purity Personified. Krishna even mentions that Arjuna's mortal mind cannot comprehend all that he is, so Krishna briefly gives Arjuna divine sight so that Arjuna can comprehend. Arjuna still can't handle it, and begs Krishna to retake human form.
Played straight in Judaic and Talmudic literature, which says that God is incomprehensible. Oddly enough, some Kabbalistic poems describe him as though he were a human king, though the rabbis dismiss this as an elaborate metaphor.
This is exactly what happened to Dionysus' mother Semele, one of Zeus' lovers; Hera tricked her into doubting that he was truly who he claimed to be, and she insisted that he reveal his true form. Due to an oath he made to fulfill a promise to her, he had to comply. He managed to save her unborn child however, placing him under the skin of his thigh until he could be born.
In The Qur'an Moses asks to see God, who replies that the sight of Him to a living mortal would be too much... but He will reveal Himself to that mountain over there — which immediately crumbles to dust.
In the theological theory of Pandeism, it is proposed that those who are somehow able to contact the mind of our Creator as it unconsciously underlies our Universe find that experience so incomprehensible that their tiny human minds automatically defend themselves by interpreting such encounters as conscious communications from culturally familiar conceptions of gods, thereby explaining all revelation and scripture.
Tabletop Games
Dungeons & Dragons has the Obyriths, the primordial race of demons spawned by the Abyss eons before life arose on the Material Plane. Their bizarre, horrifyingly-alien appearances grant the Obyriths an ability called "Form of Madness," which causes anyone who so much as glances at them to be afflicted by an oftentimes permanent type of insanity (phobias, feelings of being consumed by insects, etc).
Pale Night, the so-called Mother of Demons, is ancient even among the surviving Obyriths, but lacks the "Form of Madness" rule. She appears as a feminine figure wrapped in a white shroud blowing on a spectral breeze, which occasionally shifts to almost reveal what's underneath. This is neither her true form, nor a conventional illusion - instead the veil (which she can suppress with some effort) is a sort of cosmic censor, because her actual appearance is so horrifying that reality itself refuses to accept it. Pale Night's "Truth Behind the Veil" rule means that anyone who gets a good look at her true form must make an immediate (very high) saving throw; success means that the character's mind refuses to comprehend what they're looking at. Those who fail die outright, and if revived remember nothing of what they saw beyond a feeling of sheer horror.
Even some incredibly powerful forces of Good cannot be viewed safely by mortals. The Book of Exalted Deeds sourcebook mentions Zaphikiel, the greatest of the Hebdomad and the ruler of Mount Celestia. Only the gods themselves and the other Hebdomad can look upon him safely; anyone else who does so is said to be consumed by his overwhelming radiant energy and destroyed uttely. (Or maybe ascended to a higher form; it depends on who you ask.)
Predators, a book for Werewolf The Forsaken by White Wolf, introduces a being known only as the Unseen, which is Exactly What It Says on the Tin. It's said that its form is so blasphemous that reality itself refuses to show it (just like Pale Night). The Unseen is uncannily good at hunting werewolf packs, to the point that some suggest it's a weapon created by a werewolf-hating Eldritch Abomination. About the only way you learn of its presence is when your guts spill out of a seemingly spontaneous slice in your flesh.
Also Hell, as presented in World of Darkness: Inferno: a place comprised of so much depravity, so much sin, that the human (and supernatural) mind is unable to cope with it, and tries to resolve it into a Hell it can comprehend. Hell's corruption is so pervasive, even looking at it triggers a check on the Karma Meter, as it worms its way into your soul.
Mage: The Awakening presents magic in general and the Supernal particularly as this. The actual underlyign processes of magic are beyond human beings' ability to understand, so there need to use metaphor and symbolism to compose their spells. For those few mages who become capable of entering the Supernal itself, it's necessary to expend great effort to force it into a comprehensable symbolic form, or else unfiltered contact with it will utterly obliterate the mage. One of the goals of Ascension is to achieve a state in which true perception of the Supernal is possible.
Video Games
The Trope Namer is EarthBound. "You cannot grasp the true form of Giygas' attack!" It's a tradition of the series's final bosses.
The Masked Man may also have this attack in the form of a laser attack that the game doesn't even say anything about.
In Pokemon Mystery Dungeon: Gates to Infinity the Bittercolds attacks are implied to be this. Ontop of the Bittercold being an Outside Context Villain, it also uses attacks never seen in the Pokemon franchise before, hits the entire room, can confuse or vastely lower your parties stats, and the names of said attacks don't appear in the message log at all.
The power of Houjuu Nue from Touhou is this minus the Go Mad from the Revelation part. She can also imbue other things with the same characteristic by placing a "Seed of Non-Identification" on them, although knowing what the actual object is prevents it from working.
An example of Truth in Television, but here because it's caused by one: as said in the Bullet Hell page, in Touhou's Imperishable Night, some parts are so complex that your brain will actually stop interpreting data on some parts of the screen, and you can feel it happening.
When the time gets really low, some patterns are made to get very hectic; some spellcards aren't designed to be timed-out, which is what happens when they aren't beaten before the timer zeros. These final forms in the last few seconds are so intricate that they defy comprehension at times.
Team Fortress 2's Mildly Disturbing Halloween Mask "appears as a moldering, eldritch veil of such manifold depravity, the human eye will not process the sheer enormity of its malevolence, and out of self-preservation will merely show you a brown paper bag with a team colored face painted on it."
In The World Ends With You, it's impossible to make out the Composer's exact features, even though you can clearly tell who it is. He appears in a shroud of white light, and the artwork is sketchy and hard to focus on.
Parodied in Another Day, where it's explained that the appearance of a certain character is entirely because the player refuses to see the truth.
The Patriots, when they finally speak, claim this status in Metal Gear Solid 2. In fact, they say they're the embodiment of the collective will of the United States itself. They're a pretty Unreliable Narrator, though, and this was debunked in Metal Gear Solid 4.
The Wave Existence from Xenogears is a fourth-dimensional being that humans are unable to comprehend, and he appears as a vaguely star-like... thing from which waves emanate similarly to the ripples on a pond's surface.
The attacks of the Orochi in The King Of Fighters involve a lot of whole-screen flashes and invisible hits—but more mysteriously, the special moves are unnamed. (... as long as Orochi's clone Mizuchi doesn't count).
In Shin Megami Tensei Strange Journey, all demons are Invisible to Normals. When a third (and not entirely benevolent) third party grants the Investigation Team the Demon Summoning Program, they can "see" the demons... as blobs of unidentifiable static who speak only gibberish. You must fight and defeat these foes in order to identify them and be able to translate their speech.
And even then, the master, creator, and lord of the Schwarzwelt, as well as the mother of all life on the planet, radiates such immense power that it's utterly impossible to recognize its form. Only by receiving the "brilliance" of a traveler of the Schwarzwelt can you get a glimpse at its true form.
The bonus boss Yggdrasil has the ability to do something "almost imperceptible" (i.e. freeze time and attack). Basically, you've been struck so fast that the attack literally took no time at all. Naturally, you can't defeat it until this ability has been nullified.
Word Of God says that this holds true for the night sky in The Elder Scrolls. Mortals can't comprehend an infinite plane of existence enclosed in another infinite plane of existence which itself is enclosed in another infinite plane of existence so it all appears as a solar system.
This also applies to the eponymous scrolls, as what little you can see of the one you find before it blinds you for a few seconds is a set of strange runes and writing, when they're supposed to hold the world's entire history.
Including its future.
Devil May Cry 4 has Pandora's box, a Morph Weapon with 666 forms (not all useable), despite turning into a throwing glaive, a rocket launcher, or amissile platform its most damaging attack is simply letting the box drop open, revealing the contents inside to everything in front of Dante.
Final Fantasy VII has the ???? skill. That's right, even the name of the ability can't be determined. The effects of the spell is pretty nutty too as it only shows a weight with a question mark on it before dealing damage to the target.
Possibly due to the fact that it's hard to reduce its core concept to a few words; it deals damage equal to the amount of HP the character has lost in comparison to their max HP. "Revenge" was one name for the attack, but in Final Fantasy IX it was Played for Laughs, having the name "Pumpkin Head."
One of OFF's endings implies there's something like this going on in regards to The Batter. Sure, when you control him, you see just a man with baseball attire and a bat, but when, in the Judge's ending, you're using the Judge against him, what you see then is a monstrosity that could only be called humanoid in the vaguest sense of the word, wearing his same (perfectly fitting, which could argue against a transformation) baseball player attire. In the end, you never know if you, the Judge, or neither, ever saw the Batter properly.
Eternal Darkness had a moment where Anthony, suspicious of the person telling him to deliver a scroll to Charlemagne the Frank, opens the scroll and catches a glimpse of a strange symbol before being Blown Across the Room by the power of the spell drawn on it.
Visual Novel
Tohno Shiki of Tsukihime can see the 'death' of anything that has a flaw, but since human brains can't truly comprehend death as it applies to nonliving things, Shiki has to struggle to kill inanimate objects. He can even kill conceptual things like time or disease, although this places so much stress on his brain it nearly kills him. There are also beings who simply have no 'death', and thus cannot be killed, such as Arcueid during the night (which Shiki finds out to his chagrin during Ciel's route.)
Featherine Augustus Aurora from Umineko: When They Cry is an interesting take on this. While not really an Eldritch Abomination herself (we think), the form she assumes can vary. Being a witch of untold age, she had to create a horseshoe-shaped device that hovers around her head. This thing not only contains all of her memories, but even her physical appearance. According to Lambdadelta, it once got dinged in the past, abruptly changing Featherine's personality and form.
She can also use the power of You Cannot Grasp the True Form to initiate an attack in a similar vein to Giygas/Giegue. As the Witch of Theatregoing, she can literally stop time, rip out the script of a world and rewrite it. In the eighth and final book when she "fights" Lambdadelta, she starts from the end of the incoming fight scene and works her way back, only to the part where she deals a rather brutal finishing blow to Lambda. She doesn't even write what killed Lambda, deciding to think it up later. When time resumes, the poor Witch of Certainty suffered just as Featherine wrote and had no idea what just happened before perishing, the narrative almost quoting this trope word for word.
It gets better: Featherine isn't even the genuine article, but rather an Author Avatar of Ikuko Hachijō.
Bernkastel and Lambdadelta themselves might also qualify for this trope. The former is actually Ikuko's pet cat who takes the form of an older Rika Furude in the meta-world, and the latter is literally made out of candy.
The people at Nitro Plus made the brilliant decision in Saya no Uta to never actually show any clear shots of the monster(s). You only ever get to see individual limbs or extreme close-ups of certain body parts, with most of it being covered in darkness. What you get instead are detailed descriptions that paints mental images in your head. They realized that the true form of the monster would be more horrifying if the reader could only imagine it, and never actually see it. After all, to show the monster would mean that its looks were comprehensible. For it to be a true eldritch abomination however, it must be unimaginable.
Web Originals
Orion's Arm takes a slightly different approach. Understanding the mind of the archailects is impossible for a normal human. And actually understanding their physical form is pretty difficult too because they exist as multiple planet sized objects.
A good many SCPs are likely to qualify, although most are written as mundane things with strange properties, rather than strange things appearing as mundane things.
The most prominent of these would probably be SCP-055, which is a... thing. Anybody who sees it will completely forget about it within a few minutes. Anybody who hears or sees secondhand details, including picture and video, about it will also forget about those within a few minutes. The object is classified as Keter (most dangerous) simply because the Foundation doesn't know if it's dangerous, specifically mentioning that it could have killed hundreds of personnel in the process of getting it and they wouldn't remember any of it.
The Narrator in Shell tries to describe the Eldritch Abomination, but cannot grasp its true form when drawing it.
In Homestuck, the Horrorterrors are psychically percieved by humans as adorable squid creatures (about whom a cartoon is made) due to this effect.
It is implied in The Slender Man Mythos that this is one of Slendy's characteristics, given that he has been know to grow Combat Tentacles, his use of both On and Off Screen Teleportation, and taking into account the lack of distinguishing (read: ANY) facial features.
In a Creepy Pasta called "The Cave", there is the Eldritch Abomination known as the Jackal. The closest to a description the narrator manages to provide when it is seen is that whereas its depiction had been scratched out from pictures on the walls before, looking at the real thing is a lot like looking at those pictures, because all you can see is still something blurry and formless.
The portals in The Salvation War are very hard for anyone to really comprehend what they are seeing, describing it in completely contradictory terms (for example, one character notes it looks both parallel and perpendicular to the ground). It is mentioned at it at least a seven dimensional object, and what is seen is a best the "shadow" of the real thing.
Western Animation
Robin from Teen Titans sees the entrance to the afterlife as a regular wooden door with LIFE AND DEATH written on it.
Which is taken directly out of one of the comics when Beast Boy and Raven venture there. They even make a remark about it;
Beast Boy: I can't believe the afterlife has a sense of humor.
Raven: Yes, it disturbs me as well.
In one episode of I Am Weasel, Weasel and Baboon use a bike so fast it exceeds the speed of light in which they find in Another Dimension where the living beings look like ham. I. R. Baboon tries to eat one even after the beings explain they aren't really ham, they simply appear as such to their minds.
One episode of Invader Zim parodies this with the Meekrob, who fly into Dib's room in the form of strange, glowing aliens, and then inexplicably transform into giant floating sneakers.
After getting crap for using A Form You Are Comfortable With, an alien on The Venture Brothers got mad enough to show them his real form. All the audience got to see was that it revealed itself by ripping its "face" open down the middle, had flashing lights, tentacles, and was enough to make a (mentally handicapped) character crap his pants.
The alien Vok in Beast Wars:Transformers capture Optimus Primal and communicate with him. But to do so, they first scan his memory banks for what he would consider a figure of authority —they choose to manifest as the disembodied head of Unicron. They're actually creepy glowing energy skull things that do very little.
Real Life
The color magenta does not exist in the human visible spectrum, and is instead made up by the brain to bridge the gap between red and violet. Explanation.
Also to a lesser extent green. The wavelengths that trigger the "green" receptors on your retina also elicit a slight reaction from the "red" receptors. So in order to see true green, you would first need to be incapable of seeing red.
It's even worse than that. We have three kinds of color sensors, each of which picks up a variety of wavelengths, divisible into three pairs, Red and Green, Blue and Yellow, and Black and White. What 'color' we see is calculated as an average of all three inputs. For an analogy, sight is like how television and monitors create all kinds of colours through combinations of red, blue and green. Most colors are thus retinal stimulation translated by the brain as illusions. It's theoretically easy to force people into The Matrix by strategically implanting nanomachines in their occipital lobes.
To a limited extent it also depends on cultural values. If a language and culture has a bigger difference between colors, people in that society are better able to distinguish colors. This goes the other way too, as people who lack distinctions for colors are unable to recognize differences between them.
Sex is a factor too, as studies have shown that women can usually discern subtler differences in color than men.
Even worse, try to describe colour as you see it to a blind person.
Probably related are images taken by telescopes (or other instruments, for the case) designed to work with wavelengths that do not correspond with visible light, like Spitzer (infrared) or Chandra (X-Ray). The images of Space Clouds that we see that have been taken by them are actually processed false-color images, so we can see them with our eyes and if they were sensible to those wavelengths while we'd see something more or less with the same aspect (ie: an infrared-bright region of star formation or an X-ray emitting gas cloud) , etc, their colors (to give that a name) would be quite different. It's worth to remember that colors do not actually exist and that they're just the way the brain represents the different wavelenghts of light when they hit the retina and has to process them.
Human sight can only register tridimensional objects. Go ahead and try to draw a point in a fourth-dimensional coordinate system. You can't, since no one has figured out how to draw the coordinate system to begin with. There are certain workarounds, for example, if we use a tridimensional coordinate system, we can "simulate" the fourth dimension with a visual identifier other than position, for example, coloring the points with their according "value" in the fourth dimension.
These brain warpers are four-dimensional polytopes. Even if you can get a grasp on them, we can mathematically conceive n-topes of any number of dimensions.
We can, however, project it into three-dimensional (and even two-dimensional) space, just like we can draw a cube on a piece of paper. That may not make it easier to understand, though. (See also Flatland.)
This is because fourth dimensional space allows for the overlap of three dimensional spaces. To put it it in easier terms, a 2D plane is filled up with infinite lines in any which direction. A 3D space is filled with 2D planes in any which direction. A 4D space is filled with 3D spaces in any which way.
And optical illusions reveal just how much of what you see is manufactured by your brain to make up for a lack of comprehensible visual info in the "real" world.
People who get retinal burns (because of handling lasers or arc welders carelessly, for example) get additional blind spots in addition to the natural ones. The brain input-processing mechanism conceals these spots and the afflicted human thinks he's perfectly okay... until his entire retinas are burned, and voila, he's suddenly blind.
There is actually a way to "see" your blind spot: cover one eye and look at a page of text (this page, for example). The text that falls within your blind spot will register as a blurry spot of grey.
Not to mention that everything visible is manufactured in your mind. Reality is actually 99.9999999% empty space filled with billions of entities incomprehensible to the human mind.
It goes further. The left hemisphere of your brain, which is responsible for things like language, is also responsible for "making sense" of the world. This can sometimes lead to fairly bizarre illusions when it goes wrong. For example, left side paralysis caused by brain damage, not direct nerve damage, leads to the common illusion that the non-functioning body parts belong to somebody else. The reason is that since the damage originates from the brain, there is no feedback from the limbs to signal that something is wrong with them, since they are technically totally functional. Therefore, the brain invents the idea that the limbs must belong to somebody else. In cognitive science, this is referred to as confabulation.
It is actually rather scary that a person under such an illusion is more or less incapable of understanding that they ARE, in fact, not right. They will acknowledge any arguments made by people trying to convince them, but they will not change their mind. When the brain no longer needs to delude itself, people are confused how they could have ever believed something so ridiculous. In some cases, the same defensive mental mechanism reoccurs, and people conveniently forget their previous puzzlement. And it should be noted, this happens in people who are otherwise perfectly reasonable, sane and rational, as far as it is possible for a human to be rational. So the next time you think you perceive and analyze reality in an "objective" manner, try being a little more skeptical.
As implied above, there are many spots in the realm of mathematics in which things that can be conceived via a system of axioms or functions cannot be conceived in a pure representative form.
Douglas Adams pointed out that infinity is flat and uninteresting, since it doesn't present magnitude or scale, ergo, really big things are necessary to show just how big it is. A basic example is the Googolplex, a number so large that it cannot be represented longhand, even if we filled the known universe with protons and wrote a zero on each one.
An even bigger number is Graham's number which cannot be expressed with any standard system of numerical representation including such things as exponent stacks (e.g. a^b^c^d^e...).
Go bigger. The Wikipedia article states that Graham's number is not the biggest number to be used in a serious mathematical proof. That's right, there's a number bigger than the number that cannot be expressed in this universe.
It can be expressed, as it is on that page, with recursive stacks of exponents, which are themselves used recursively 64 times, all the better to make your head explode with, my dear. Even the first of these 64 terms is incomprehensibly huge; far, far bigger than the number of atoms the Universe could hold if they were packed together as tightly as physically possible, let alone the much smaller number of atoms it actually contains. And that number is subjected to the same ludicrously fast increasing process sixty-three more times. And, heck, you could just continue past 64 cycles up to, say, a Googolplex of cycles, and then...actually, let's not go there.
Fun fact: Graham's number is the maximum limit of the number of unique variations of a particular problem. The minimal limit, at the time, was thought to be 6. (It has since been increased to 13.)
Those numbers also can't be constructed physically or computationally. Meaning they can't exist physically or even in simulation.
And now remember that all the numbers mentioned above are as far from infinity as the number 1.
As if infinity wasn't hard enough to grasp as it is, the infinity mentioned above is only the first, and smallest, infinity (generally denoted aleph-null). There are even larger infinite numbers; in fact, there are so many larger infinities that the question "how many" does not apply to the totality of them. This is because the total collection of infinities is too large to correspond to any infinite quantity. Isn't set theory fun?
Mathematicians have explained that infinity is more of a process than a value, because you can't define infinity's value other than "really large".
Related to this is infinitesimal, which is a something that can only be described as a value that is infinitely small, but still reasonably significant. It's probably first heard when taking a physics class or learning about integrals.
We don't even need to resort to very large numbers for indescribably. The amount of numbers between, say, 0 and 1 is a greater infinity than the amount of possible permutations of words in any language. This means that the total amount of numbers between 0 and 1 is more—significantly more—than the total amount of possible ways to describe numbers; therefore there must be many numbers between 0 and 1 that cannot be described.
And then keep in mind that this is true for decimal numbers between every single pair of whole numbers you can think of. And then invert that, because the same is true for negative numbers, meaning that there are an infinite number of infinities between every pair of whole numbers.
Still about mathematics, there are fractals. Their number of dimensions varies whether it's topological or not, and their "true" (Hausdorff) number of dimensions is often non-integer. The Menger sponge, for example, is an object which has zero volume and an infinite surface area. Which means that any Menger sponge you'll see is only an approximation.
For another example, look at Sierpinski's Triangles (imagine a Triforce where you replace every triangle with another Triforce ad infinitum). It has roughly 1.585 dimensions (more precisely, log(3)/log(2).
This Crackedarticle contains some examples, particularly one mental disorder that makes it so you can only grasp the form of one thing at a time.
The philosophical concept of the Platonic Cave takes this on a cosmic level: the world we are seeing is just an imperfect illusion projected by metaphysical abstractions which are named by Plato as "the Forms" (whose true form we cannot see, hear or touch, only try to make sense and interpret through reasoning). This is related to the "magenta is not real" example above, in how the light and colours that we see are just abstract electromagnetic energy waves projected to our retina and interpreted by our brain as visual illusions. A common way to demonstrate this is the famous question: Sound waves, which we recognize as music or language, are in fact nothing more than molecular vibrations that are merely interpreted by the auditory nerve as "sound", so if a tree falls down and nobody can hear it does it make any "sound"?
That last example requires a bit more explanation. All "sound" is actually a wave of pressure traveling through a medium; in this case through air. According to the laws of physics a tree falling in the woods can, and indeed must, generate such a pressure wave, and thus make a sound, regardless of whether anyone or anything is nearby to hear it. The reason this trope applies is because the human brain can't actually perceive the pressure wave itself. It moves too quickly for us to observe in real-time. We can only sense the effect of the pressure wave when it hits us, which our brain reinterprets as a "sound". If we were able to see the vibration in real-time it would probably look something like waves on the ocean. Or like this Mythbusters clip.
Go outside at night. Look up. How far away are the stars you're looking at? How big are they? And yet you go through most of your life not even thinking about it...
You don't even need a lot of stars to boggle your mind: just one will do, if you glance at the sun and try to grasp how gigantic that not-that-large-looking disc actually is.
flavour text, Magic: The Gathering
