In as few words as possible.

[Clipped and Shorn]

This relates (marginally) to the AB/X thread in which "illusions" seemed to be relevant.

How would you explain this apparent conundrum?

[DrWho]

Niether shape is a triangle.

(does that describe it fully or need I elaborate?).

[oldenough]

Thanx, that's just what i needed before going to bed, something to think about.[]

Ok, i see it...good one.

[Clipped and Shorn]

Docker Who,

You are correct sir. Good answer.

They are both sneaky quadrilaterals.

The would-be "hypotenuses" either "bulge" or "sag" to accommodate the fudging. The inside triangles (defined by the angles the tangents suggest are not equal as proposed). Anyway the really short answer is:

Magic!

(as in sleight of hand and misdirection)

-Sea & Ess

Niether shape is a triangle.

(does that describe it fully or need I elaborate?).

[Daddy Dee]

This is sort of hurting my brain now.

[WMcD]

Okay, there are two ways of observing the little fraud. Mike saw it right away but I had to ponder. Actually the subparts are triangles The gross figures are not.

I turned the laptop monitor sideways and up to sight along the hypothenus. The gross hypothenuse is not a continuous line in either gross triangle. As described by others, the one at the top one sags concave and the one at the bottom one bulges convex. visually. This is enough to make the extra square.

This works out mathematically too; but I had to convince myself. Look at the red and green triangles. The left-most angle and its resulting slope on both should be the same if the hypothenuse on the gross triange is a staight line. It can't be.

This is because on the red triangle, the slope is 3/8. On the green, it is 2/5. On the gross triangle, if true, it is 5/13. Close, but no cigar.

What is more interesting is that the cheating on slope results in exactly one square.

Pythagorus is hiding in there. Double entendre.

Gil

[mas]

For those still confused by Doc's observation, focus on the slopes of the hypotenuse (the sloped line) of the red and green right triangles.

The rise/run of the red triangle is 1/2, while that of the green is != (not equal) to 1/2. Instead the slope of the green triangle hypotenuese is ~0.75/2

Another way to do this is to place a ruler connecting the endpoints of the same line and noting the deviation.

Hope that helps...

[DrWho]

What's interesting about solving this illusion is two things: one that you get both pieces "one atop the other." How much harder would it be, if each large triangle was on its own flash card, and the subject was shown first one, and then the other, but never both at the same time? The other is that you use parallel processing to solve the puzzle. You can see all of it at once.

Actually, I solved the puzzle "serially" if you want to use that language.

To be honest, I don't know of anyone able to "parallel process" since our eyes can only focus on one thing at a time.

[Clipped and Shorn]

"What's interesting about solving this illusion is two things: one that you get both pieces "one atop the other." How much harder would it be, if each large triangle was on its own flash card, and the subject was shown first one, and then the other, but never both at the same time? The other is that you use parallel processing to solve the puzzle. You can see all of it at once. "

ME: Yes, if the images were flashed serially, one would observe a difference, one which could not be explained rationally. One would have to believe in magic. It would appear to be yet another dimension of cinematic special effects magic. Impenetrable.It would be a difference which all rationality would say is impossible or non-existent, yet the observer would be sure he saw a difference in spite of its reputed impossibility.

"AB/X is a serial and sequential challenge. Complicated sound streams are presented one after another, each forming unique phenomenal experiences, which must be compared serially in the abstract. We can't "see" the whole piece of music at a time, we must intake it in serially, not using parallel processing as we do with visual puzzles."

You point out what has always been the biggest obstacle to using a visual analogy for an auditory experience. I always get blank stares from musicians when I refer to "rests" as "ground" and "notes" as "figure", eg. a musical or rhythmic phrase being figure and ground in much the same way as in art. Remember those illusions where you either see a young girl or an old hag, that has to do with figure and ground, by the same token, I will analyze a rhythmic pattern by taking note of the pattern (shape) of the rest pulses.

0x0xx0x0x0xx say the 0 is the note hit. Then the rests pulses, the x's, express another pattern 0x00x0x0x00. If you play the notes with your right hand while simultaneously playing the rest pulses with your left hand, then one might hear or pay attention to either, just like when you either see the young girl or the old hag.

This whole area of crossing one sense modality into another is called synaethesia and has always been facinating to me:

http://www.kuro5hin.org/story/2003/2/21/144256/437

Both senses follow the principles that were presented in the realm of gestalt psychology, and as such, both vision and the auditory are subject to the same types of illusions (closures), although you do point out an enormous difference between the instantlly comparable and the serial comparable. Closure illusion is not controllable, eg. your eye/mind is hopleslessly "convinced", for example, that those alternating flashing lights on traffic signs are "moving" back and forth! The consecutive flashing of still frames at 24 frames per second in the movie is seen, unalterably, as MOTION. This is what I mean by the term "closure", it is the brain (cognitive system) which "explains" the sense data. The same system "explains" the 3 inch difference between what each eye sees as "depth". Etcetera.

Sorry for throwing around so may tangent ideas, but hopefullly it will kick on the discussion.

-Kip and Handstand

[Clipped and Shorn]

Gil,

Good analysis.

On another note, anyone who has done tile work or marquetry knows how quickly a small almost imperceptble variation in a line or the width of a cut or the width of a grout joint manifests as a dramatic effect when translated to "area". Even a carpenter knows the importance of which side of a scribed line to cut. It matters. It always seems amazing that a wall made of random rocks or a patio floor made of irregular flagstones seems like it fits together like a puzzle, it is all in the virtually unnoticeable fudging of the grout joint. The designer of this puzzle was tricky.

c8s

[jacksonbart]

.

[Clipped and Shorn]

Clipped---

Yeah,
the cool cat blowing sax and the beautiful face is a nice example of
"thing" and "no thing." Which must always exist together. As you refer
to it, figure and ground. What happens if you take all the objects out
of space? Does space still exist?

In the "gestalt" sense, the answer is yes and that brings up one of the most basic concepts in that system, the FIELD.

http://books.google.com/books?id=NWtM-L83RnwC&pg=RA2-PA28&lpg=RA2-PA28&dq=gestalt+terminology

+%22the+field%22&source=web&ots=CYZP3emtEh&sig=q5d_3qjBwvDDvr1RjBtEzFf5zsU

(you need to cut and paste together both halves of this url in order to go there. )

(my friends call my Tiny Earl (Url).

-Tiny

[mungkiman]

Which way is she spinning?

[mungkiman]

Clockwise, or counter-clockwise?

"Just the right way" is not an acceptable answer...

[Guest " "]

I'm on a mac.

Each time I click on the picture....she changes positions...and turns the other way.

[mungkiman]

It's all in your mind. Just let her spin...

[Guest " "]

it's probally alternating and actually spining in both directions....as I watched I said it was going clockwise.....my son said it was going counter clockwise.

[stormin]

Thats pretty awesome. She travels in both directions according to how I perceive her. If I focus she moves one direction then refocus shes moving the opposite direction.

[mungkiman]

Im told:

If you see her spinning counter-clockwise, you are left brain dominant.

If you see her spinning clockwise, you are right brain dominant.

If you see her as spinning only for you, you are wrong brain dominant...

Seriously, almost all children see her with their right brain, at least until they have to go to school!

Those that can see her spinning both ways are more "whole brained" than most of the population.

As a silhoette, the direction is purely ones own perception!

[klipschaholik]

The big question is will it fly?