Referring to the image in the source below please answer the following question:?

Question

http://en.wikipedia.org/wiki/Image:IsometricFlaw_2.svg

If you place a dark brown square between the squares holding the red and blue balls what floor of the structure is that square you've place on? Don't cheat by looking for clues in the text material below the image. That is, unless you're an inveterate cheater.

For more on Isometric projection pseudo-perspective see

http://en.wikipedia.org/wiki/Isometric_projection

mank As much as I try my eyes (and brain) refuse to be tamed by brown squares. Even after being reluctantly convinced that the left side of the image could be one floor they still insist on seeing (believing, I suppose, in the case of the brain) the right side of the image as 3 stories in height. Curious isn't it how terribly (yes that's the word I must choose here) easily the senses and brain can be fooled.Ier we humans get ourselves into the predicaments we do?

That last sentence should read, "Is it any wonder we humans get ourselves into the predicaments we do?"

Answer 1

OK, I didn't mean to answer this question, so I cheated. I read the text material below the image, and I read the Wikipedia article on isometric projection.

But then I'm a "literalist of the imagination." None of that material answered the question the way I would have, so I have to put in my two cents' worth.

If you place a dark brown square between the squares holding the red and blue balls, that square is on the first floor of the structure.

You see, when you put that dark brown square there, what you did was to reduce the structure to two dimensions, hence only one level.

After all, it's been only two dimensions all along, but the trick of isometric projection fooled the eye into thinking it was three-dimensional. And the foolish eye doesn't like to be un-deceived.

But that brown square will do it in spite of one's addiction to foolishness. What was standing upward in space, sorta like a building, has now become a carpet or a tiled floor (only one level, one floor). At the east end of the floor (or right side of the image) are some square tiles matching those in the rest of the image, but there are also four diamond-shaped tiles of four different colors. The eye had been tricked into thinking of them as squares seen from a certain perspective, but the brown square now tells the eye that the structure is flat. So the diamond-shaped tiles are simply that: diamond-shaped tiles. They are not squares seen from another perspective.

The eye wants to rebel. It wants to be fooled. It wants to believe it's seeing three dimensions, just as some folks want to see "weapons of mass destruction" in Iraq or angels on the head of a pin.

But brown squares tame the eyes. "Pay attention," they say. "Don't let yourself be deceived yet again."

OK, some deceivers are cleverer than others. M. C. Escher is a Master of Deceit. Call him charismatic. Hear his angels, crying, "Holy, holy, holy." What's two-dimensional is really three-dimensional, he insists. And we believe.

"We believe; help thou our unbelief."

LATER, IN RESPONSE TO ADD'L DETAILS:

The question is not how do we tame our eye into seeing this as two-dimensional (clearly, it is two dimensional). The question is how did our eye (and mind) get tricked into thinking it was anythiing but two dimensional.

So go back to the raw materials. The design, if you add the brown square your original question posited, will consist of six brown squares and six, let's call them, off-white squares. Then there are four diamonds, one of which is a matching brown, one of which is a matching off-white. The other two are a darker (or shadowed) brown and a darker (or shadowed) off-white. The rational empiricist will see these "as they are"'; that is as sixteen flat shapes (I analogized them as tiles on a floor), all put together in a two-dimensional design.

The "believer," conditioned by years of imaginative visions (or imposed doctrine--take your pick) will see the four diamonds as if they were squares but not seen literally as squares because of "isometric projection."

So Reason and Empiricism tell your mind that what you are seeing is two-dimensional, twelve squares and four diamonds; but Imagination and Faith (or conventions and doctrines, if you will) tell you that what you are seeing is three-dimensional, sixteen squares. Common sense, and that last brown square, simply won't let the Vision stand in its three-dimensional splendor.

So it flattens three floors into a floor, or it sends you into orbit.

Now, William Blake with his four-fold vision (or the little lame boy in "The Pied Piper of Hamelin") have the joy (or problem) of seeing it both ways. But people like them, who see it both ways, will always be outsiders among both the "scientists" and the "believers." So they have to expect to be treated like Outsiders. They are Addicts. Addicted to signifiance, to multiplicity, to Infinity. "Weave a circle round him thrice," people will say, "and close your eyes with holy dread." In other words, "Don't fall under the influence of this Outsider, this Addict."

"For he on honey dew hath fed / and drunk the milk of Paradise."

But to the Outsider and those who listen to him, to be able to see the design simultaneously as two-dimensional and three-dimensional, not one or the other, as having multiple meanings, even infinite meanings, is Paradise Regained.

Or in William Blake's terms, The Marriage of Heaven and Hell.

So be it.

Answer 2

You are comparing a 2 dimensional square to measure a 3 dimensional problem. that brown square may seem to connect with the floor 2 floors down - but actually - it just lines up with that floor from the perspective we have.

There is a 2 floor difference.

Answer 3

The squares that the two balls are on are apart by 2 squares up and 2 squares across so you couldn't place a dark brown square between them. Nice puzzle thanks!

Answer 4

On the second floor.

Answer 5

It could be either, like one of those infinity and surreal pictures. It could only happen tricking the eye.

Answer 6

im sorry i cant answer the question,im an inveterate cheater..

Answer 7

It is not on any floor, but floating in space.

Answer 8

the second