Vsauce, I’m Jake and on a recent flight I rewatched the fantastic Christopher Nolan
film Inception.
In the movie Joseph Gordon Levitts’ character mentions “The penrose steps.
The infinite staircase.”
And that got me thinking about impossible objects, which the penrose steps or impossible
staircase are.
So, I decided to 3D print some.
Impossible Objects are shapes that form in an inconsistent way creating a visual illusion...something
that deceives our mind by producing a false impression of reality.
And if you’ve played the video game Monument Valley, it is filled with those sorts of illusions.
So let’s look at a few examples we printed starting with
This is the impossible staircase.
An endless loop of steps going up, then back down, then back up and so on and so forth.
At first glance it seems logical, we understand what a staircase is and how it functions but
it is connected in such a way to create an impossibility.
Once we rotate the object and change the specific viewpoint, the illusion is revealed.
With every impossible object the most important part is perspective and lighting.
It only works if you are looking at it in a very specific way, For the effect to exist
in real life you need to have one eye closed, limit your depth perception, or be looking
at a 2D image through a camera lens like you are right now with this video, and that also
applies to what we generally think of as a 2D image, one that is drawn.
In the february 1958 edition of the British Journal of Psychology, a paper by Lionel and
his son Roger Penrose was published describing a creation of theirs...the Penrose Steps,
the impossible staircase, a structure that is “acceptable as representing a flight
of steps but the connections are such that the picture, as a whole, is inconsistent.”
Also in their paper they talk about how two-dimensional drawings can be made to convey the impression
of three-dimensional shapes.
It can be used to induce contradictory perceptual objects.
And no one was better at that or more widely known for it than M.C.
Escher who, two years after the Penrose’s paper, created Ascending and Descending showcasing
that particular impossible object in his work for the first time.
And speaking of M.C.
Esther, he imagined and drew a multitude of impossible structures and objects, one of
my favorites is an object he created called
The Impossible Cube first appeared in Esther's piece Belvedere.
Down at the base of the steps on a bench is a boy holding the cube.
And in real life, it looks like this.
The beams at the joints are intersecting with the horizontal crossing sections, weaving
in front of and behind.
If you stare at it long enough, looking at the object as a whole, your mind becomes tricked
by what side of the cube is in front and which is in the back.
That is until we move it.
It is incredibly reminiscent of another type of perspective illusion that I’m pretty
sure you’ve drawn at least once in your life, the necker cube, which is also in Belvedere
at the same boy’s feet.
It is an ambiguous line drawing.
Even though it is a 2D object, it’s depth changes.
Is this the front...or is this?
It creates a bistable percept, a perceptual phenomena where there are unpredictable subjective
changes.
YOU NEED CONTEXT or else a shape could be in any orientation.
When our perception disagrees with physical reality, we say we have experienced an illusion.
A visual illusion is not really there in the image.
Our mind makes it “real”.
All of these objects I am showing you have been lit in such a way, and filmed in such
a way to make it look like they are all on the same plane, that is to say, that there
is no part of the object out of focus even though they do have depth.
In essence we are filming a 3D object to look like a 2D object to give the illusion that
it is 3D.
And one of the best examples of this is probably the most famous Impossible Object.
The Impossible Triangle or Penrose Triangle, was first created by swedish artist Oscar
Reutersvärd in 1934 and, separately, by the Penroses in that same Impossible Object paper
from the 1950s.
In it they say that the lines of the drawing are connected in such a manner as to produce
an impossibility.
Yet, here it is.
When features or objects are touching they tend to be viewed at the same distance.
It looks like every surface, every connection is on the same plane creating what appears
to be one solid object...even though it isn’t.
So what’s happening?
Impossible objects are perceptual paradoxes, objects which cannot exist.
And we tend to use the term visual illusion or optical illusion to describe them but that’s
not always correct because, as we discussed before, the cause is beyond our eye.
Here we see 4 large circles with smaller circles filling it.
Ok, nothing too crazy but what if we turn some sections in these circles blue?
What do you see?
A square maybe even though there are no lines in between the separate larger circles to
tell us there is a one, there are no physical boundaries but yet our mind is making them.
Let’s look at another example.
We have these objects.
It looks like there is depth even though it is a 2 dimensional image.
If I asked you what those two shapes were you would probably say two rectangles with
one beneath the other.
But looking at it, why does our mind assume this?
Why not a rectangle with two squares on either side?
There is typically a degree of predictability or expectancy from one glance to the next
in the visual world.
Things look as they do because they are what they are.
Or are you?
Hey Jake.
Oh hi Eric.
We are intentional beings who are projecting our expectations into the future.
We usually see what we expect to see.
It’s Empiricism, the philosophical approach that "all information is derived from sensory
perceptions and experiences".
We use information from the past to predict the present.
For example, we say this is a table because we were told that this is a table.
You don’t need to see the legs of it to know that.
It has become an object.
Just like this book is an object.
And when taken individually, the words in the book are objects as well.
It’s Gestalt Psychology.
Gestalt in German means “shape” or “form”.
And in short, Gestalt Psychology is that we perceive objects as a whole rather than as
parts.
Our perceptual system organizes what we see into groups which brings us to the five grouping
laws: The Law of Nearness or Proximity, of Similarity, of Good Continuation, of Closure,
and the Law of Common Fate.
We saw the Law of Nearness with those 4 circles that when areas were colored, created a square.
Where objects near each other tend to be seen as one.
But the two laws that factor in the most with an Impossible Object are the Laws of Good
Continuation and the Law of Closure.
These two Laws can be seen in all 3 of the impossible objects we looked at but lets focus
on the impossible triangle for the Law of Good Continuation, where the lines of the
object come together to be seen as one unit.
And with the Law of Closure, it states that when a figure has a gap, we tend to see it
as a closed complete object.
Like in the case of the impossible stairs.
If you want some more illusions, I would highly recommend checking out Michael’s video on
the Sydney Opera House Illusion on our DONG channel.
Michael, Kevin, and I are making two videos a week there and it is full of Saucey goodness.
There is a link in the description to go give it a look.
Now, just for fun, here is one more illusion we made.
Not only does it look like an impossible triangle but something else is happening.
It looks like each cube that makes up the triangle is coming straight at us even though
we know it is a trick so it can’t be.
And of course, it isn’t.
We tend to have the visual assumption that objects are more likely to be convex, bulging
outwards, instead of hollow.
And a lot of that effect is accentuated with lighting.
Now these illusions challenge us to disagree with what our mind is seeing.
We are aware we are being lied to, but it is hard to pinpoint why.
It is that rare moment when we know our brain is wrong but how do you convince yourself
that yourself isn’t seeing what it is?
Because of what we know, what we’ve been told, we tend not to question what we see,
we rationalize it...If it can’t be real than how is it in front of me?
Everything is an illusion, we’ve just been conditioned to give it a form, to make it
an object.
And, as always, thanks for watching.
If you’ve seen my videos before you know I love and use the site Skillshare who are
supporting Vsauce by sponsoring this episode and by checking out Skillshare, you can support
my videos as well.
They are a wonderful online community that offers over 20 thousand classes on things
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I’ve taken courses on color correction and photoshop using Skillshare but if you want
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Introduction 3D modelling in Blender class.
Blender is great because it is free, open source and pretty full featured so you can
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That’s a pretty good deal and I love you.