"What is actually happening is that the viewer's response is
DIFFERENT than that which OUGHT to follow from the rules of perspective.
If you draw two moons the same size, they ought to be perceived by the
viewer as having the same angular size. If you draw a smaller moon in the
background, the perspective lines you used in composing the drawing are
intended to ensure that the angular size falls off with distance toward
the horizon in a linear fashion."
"If in fact (after you've erased the perspective lines) the
viewer "sees" the background moon AS IF it were too big to be
contained within the perspective lines, you have an illusion."
Mike: THAT CAN NEVER HAPPEN, EVER! If they already look like
they fit between the red perspective lines, they will remain looking so
after removing those lines. To do that illusion, you'd have to invent and
add some kind of additional image to the drawing (unknown by anyone what
that would be, if anything even can be invented other than by Escher, if
even he could). You might as well say "suppose I've poured 2 cups
of water into one cup." The supposition is impossible (except for
people who will "see:" what they want to see). In this debate,
you tend to come up with such things with no obligation to provide serious
evidence for them before you incorporate them into your unshakable views.
But if you send such a picture, I will change my mind.
But I'll go along with you ANYWAY, for now.
In summary: We don't see anything "out
there." All we see is what our inside mind tells us we see. We don't
even see what's on the retina. The mind first measures, compares and then
"interprets" what is on the retina. Instead of letting us see
exactly what's on the retina, it "tells" us to see what it has
interpreted from the retina's information. The mind "assigns"
sizes and distances to things, based on
* past experience,
* knowledge/learning, and
* from perspective cues on the retina.
Not *just* the latter. If the cues are contradictory,
then the mind is tricked or is forced to come up with an interpretation
that is an "illusion" despite what the retina has
on it. That's the way we see.
Seeing is not a perfect process. But it's
good enough to keep us from tripping over stuff and from realizing that
we are -- except for "interpretations of the mind," -- *really*
in the dark and only looking at the insides of our own head.
The less we know about something or its actual
distance (how can we "see" or visually measure the moon 240,ooo
miles away?) -- then the more subject to an illusion (or mistaken interpretation)
On the other hand, the more we know about
objects we see, the more that knowledge plays a role in the mind's interpretations
of distance and size ("believing is seeing" rather than just
"seeing is believing"), and the more accurate our "eye"
becomes about measuring reality.
Seeing is a learned [and ongoing learning]
process, rather than just biological (i.e., lenses, irises, retinas, etc).
The pics will show this.
So -- on with my reply to this in general.
You don't seem to know the meaning of the word "illusion"
in perspective. Perspective cues always play "tricks"
on the eye. Some are more extreme or dramatic or based on clues impossible
to find in reality (Escher) that the eye cannot deal with without causing
an effect that defies, for example, the actual subtended diameters in comparison
with another actually identical image, or that shifts conclusions of depth,
distance, size so they cannot apply to all parts of the drawing consistently
(because, in Escher, for example, they are defying physical law, "object
permanence," or the like). But where they apply -- they DO
apply consistently. Always. Except for figure and ground shifts (vase/faces)
-- which are meant to apply in the same place).
You attach unspoken or mystical attributes to the word "illusion"
that it doesn't have.
Now here's my proofs:
If I want to draw three identical streetlight globes screwed to a wall,
I will draw this picture "A" below. [If you wish to say that
since this is "regular" everyday "ordinary" perspective,
and that therefore there is no illusion, that is okay with me, but actually
it's dead wrong. There is always an illusion. But let it go for the purposes
here. We'll say there is no illusion, throughout this exercise.]
Now I have three equally-sized globes fastened to the wall with 3 round
identical fasteners, all shown in perspective.
Now I want to draw another pic, but this time I want to make the middle
globe look bigger than the outer two globes.
All I have to do is make the middle globe larger. So I draw
it larger -- and ANY size larger that I draw it will do -- no matter
WHAT the size I draw it, it will look (in normal interpretation of a perspective
picture) "larger" than the other two.
So I now draw this:
Compare back & forth pic A and pic B. The middle globe is bigger
Or -- I could draw yet another still larger-size globe in the
Again, switch back and forth from pic B to C or from pic A to C.
In any of these cases, the middle globe has been made larger than it
was originally in pic "A" where it was depicted in correct perspective
as being the same size as the other two globes. So in pic B and C, by perspective
interpretation of the drawings, the middle globe looks larger than
the other 2 globes there.
Now here's the rub. REMEMBER, we are saying that all
three pics are drawn in standard everyday normal perspective where (as
you prefer) there is no "moon" illusion nor other "optical
Nothing bizarre, alien or new in some mysterious way that might trigger
an electrifying visual illusion or effect has been done to this everyday
ordinary perpective exercise except to change the size of the middle
The fact that in picture "C" the middle globe just HAPPENS
TO BE THE SAME SUBTENDED DIAMETER OF THE FIRST GLOBE is --- IRRELEVANT.
It's just another increase in the size of one object in the
perspective field and the perspective clues have no reason not to work
normally. It could have been ANY increase in size.
Unless you wish to claim that making it the same diameter as the first
globe does magically change how perspective clues work? But if they work
at all for the observer in a normal way it will be seen as described --
by an observer who will not concentrate on trying to measure the flat screen's
absolute diameter sizes and wash away the cues surrounding it like we try
to wash out the sound of a motor or fan in the room when we try to read,
But now, you could give up the wrong notion that perspective clues
do not create illusions. If you do, then there IS an illusion in
all three pictures. In the first, by illusion, the 3 globes all look equal,
even tho' each is smaller from left to right..
In pic B, the middle globe looks larger than the others, but due to
lack of enough distance clues, it is a little ambiguous whether
it is clearly "looking" larger than the first globe. The
round rivet holding the middle globe to the wall tends to define its size
Adding our "man" image -- in perspectively smaller sizes
standing next to each globe would completely end the ambiguity. But I won't
bother to draw another picture to prove that. You do it.
There is in pic C no doubt that a normal interpretation
of the perspective cues there makes the middle globe largest of the
three without ambiguity.That the first and middle globe have the same actual
diameters is not grounds to believe there is any "special"
illusion here, as it looks bigger than the 3rd furthest globe for the same
reasons it looks bigger than both of the other 2 globes: Namely, the
"illusion" of perspective interpretation of distance clues.
There is no reason in the picture to presume that any special optical
illusion other than perspective itself takes place. The identical retinal
diameters of two globes does not provide that reason, unless one reaches
for some mystical unknown process that equal subtended diameters in a picture
can somehow activate and create a mistakebn interpretation. I won't buy
it. I can prove it otherwise, anyway.
If there was any reason to conclude an optical illusion conflict
of an Escher type, it would only be due to failure of the perspective
information to unambiguously nail down the distance of any object from
the others. And that's all. That aspect of insufficient information exists
all the time in nature and reality; hence we often mistake the size and
distance of objects as a matter of course. The ambiguity in pic B could
also exist in nature.
A lack of distance information, misleading information, or a lack of
perpective clues is not necessarily an optical illusion. Ambiguity does
create mistakes in perception. If you want to call that "illusory,"
I don't really object much. Often other information (prior knowledge, bias,
sound, or expectation) can prevent the ambiguity from producing a mistake.
(E.g., headlight or flashlight?)
Learn how to find the lacking distance info, fix that, and the "mistaken"
interpretation or "illusion" disappears [or appears]. -- For
those not seeing only what they want to see.
A QUICK TREATISE ON SEEING
with no new pictures:
An exact formula that proves that there is no "special" illusion
involved in the moon or any other size-illusion, or any other illusion
of the S.A.Y.E. (Subtended Angle at Your Eye), actual or apparent.
When the mind interprets the 2-d retina image, it's an exercise in
true Einsteinian relativity. Everything we see is measured and related
to everything else around it. It is mutually defining (of sizes and distances):
Things are judged as further or nearer -- behind, next to, or in front
of -- bigger, the same, or smaller in size -- than each of all the other
things seen. The mind then interprets or assigns the appropriate sizes
and look to things as best as the distance information will permit.
Therefore, in picture "C," in which the illusion you felt
was very strong, the illusion is as follows. (Each starred * sentence is
like an exact formula or axiomatic statement):
1* An object that looked bigger (middle globe) actually subtended no
greater diameter than the smaller-looking object (the first nearest-looking
globe). I.e., It only APPEARED to be bigger (due to cues that locate its
perspective distance). Relatively speaking, we MUST and can ALSO SAY:
2* The object that looked smaller (the nearest looking-globe) actually
subtended no SMALLER diameter than the bigger-looking object (middle globe).
I.e., It only APPEARED to be smaller. Therefore, the "illusion"
could be understood to apply to EITHER of the globes that have the actually
same diameters (S.A.Y.E.). Thus the illusion could involve either of TWO
objects or globes. Which one "owns" or causes the illusion? Which
one is producing the mistaken or "apparent" SAYE? Is the middle
globe that looks "larger" the mistaken one? Or is the frist (nearest)
globe that looks smaller being seen as mistakenly smaller? How do you find
out? Or -- maybe the question itself is a false question, based on a wrong
assumption that the illusion is "special" or caused from a special
occasion or circumstance or "ownable" by only one object or one
comparison? Neither the smaller or the larger SAYE is the mistaken or "apparent"
SAYE, until you answer this: Would there also be other such "illusions"
when the actual dimensions or actual diameters of this object (or any other
object in the picture) is compared to ANY other objects' diameters or dimensions
in the picture? The answer is: Yes: An alteration of apparent SAYE takes
place in every comparison -- IF distance cues are DIFFERENT for the two
compared objects. It is irrelevant whether the actual (note, actual) SAYEs
are equal to each other, or just a fraction of each other.
3* By natural logical extension, EVERY other globe or object's dimension
in the picture is similarly involved in the same KIND of illusion, whether
the ACTUAL S.A.Y.E. of the object is equal to, or just a fraction/multiple
of dimensions found in these other other objects. Thus, the 3rd furthest-looking
globe is similarly involved in an illusion: If its apparent SAYE must be
drawn, to meet the demands of perspective, at 1/3 the diameter of the first
globe [in order to pictorially "appear" to be a "same-sized"
globe as the first globe], then the first two formulii apply to it (and
to all other objects), except we substitute different dimensional relationships.
To wit, for the third globe we'd say:
--An object that looked bigger (middle globe) actually subtended no greater
than 3 times the diameter than the smaller-looking object (the third furthest-looking
globe). I.e., It only APPEARED to be more than 3 times bigger.
--The object that looked smallest (the furthest-looking-globe) actually
subtended no less than 1/3rd the diameter than the bigger-looking object
(middle globe). I.e., It only APPEARED to be less than 1/3rd the diameter.
Therefore, and so on:
4* Whatever the absolute or actual SAYE of any object, it is ALTERED
by the mind's judgement of size to suit its relationship to other objects
-- as long as those objects are depicted at a different "distance"
from it -- hence the altered or "apparent" S.A.Y.E.s ARE usually
different from the actual SAYEs.
5* Only those compared objects depicted as being apparently the SAME
distance from the eye will be unaltered and show no mistake or illusion
or difference between apparent and actual SAYE.
6* In ALL cases, if you remove ALL the distance clues (i.e., no horizon,
convergences, nor any other form of perspective grid) , the SAYE of every
object is seen and interpreted both by the eye, and the mind, with its
ACTUAL S.A.Y.E. No illusions can take place without distance cues (intended
cues or accidental ones). In any perspective scene, distance cues serve
as a form of visual "knowledge" which alters our perception [or
judgment] of the size (SAYE) of any object -- only when compared to another
object (at a different depicted distance).
7* If you then replace ALL the previous distance/perspective clues,
then every object gets re-interpreted, as to its relative size, with an
altered or "apparent" S.A.Y.E. (except as in #5*) different from
the actual SAYE depending on the influence exerted by the perspective/distance
cues and requirements. Therefore, the "perspective experience"
is an accumulation of dozens or hundreds of so-called "special"
illusions in every picture or real scene. It's just arbitrary convenience
to pick as "special" only those illusions where 2 of the objects,
affected by different surrounding distance clues, when compared, "happen"
to have the "same" actual SAYE (rather than being some fraction
or multiple of each other's size).
Pictures can be drawn to prove each axiom or formula.