Welcome to the Inconsistent Images blog. This blog is dedicated to discussing all aspects of the kinds of inconsistent (impossible) and incomplete (vague or ambiguous) pictures.
The Inconsistent Images web-site can be navigated from the menu on the left of its main page.
Please leave a comment. We would be interested in any reaction you might have.
CM
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Impossible pictures represent something that is impossible in the real world. Things in the real world do not fade out ( as in the Schuster fork)or obey 3-dimensional Euclidean geometry so that parts that are deeper can not also be joined.
ReplyDeleteWhat makes something "impossible in the real world"? If Einstein's theory is right, isn't Eucldean geometry impossible in the real world?
ReplyDeleteWhy so few comments? Is it because it is too hard to say something intelligent about this amazing site?
ReplyDeleteMaybe there are so few comments about this site because being amazed is not being critical. Maybe being inconsistently impossible is a creature too hard to fathom outside classical conceptions of the world, so people simply remain mute at the sight of it. Maybe angels fear where fools tread and nobody wants to be seen walking with fools even if they step into wonders only an inconsistent geometry can glimpse.
ReplyDeleteI think "impossbible images" are consistent in an important sense. When we perceive an impossible image, everything we perceive is consistent, and it's only when we shift our attention to another part of the image that we perceive something that was inconsistent with what we just saw, but which itself is consistent.
ReplyDelete^Anon,
ReplyDeletelocally consistent, yes, globally, no;
whilst each side say, A, B, C is consistent, the conjunction of the three is inconsistent. My "experiencer" sees the whole as inconsistent.
I guess my point was that we never perceive the whole, and when we try to our perception is always lacking detail.
ReplyDeleteM,
ReplyDelete"we never perceive the whole" I'm not sure I follow what your line of thought is. Consider the Penrose triangle, if you did not perceive the whole, then you cold not deny it as being inconsistent. That is, if you cannot see the whole, literally, and the whole is inconsistent, then you literally cannot see the inconsistency. However, you, appear at lest to be denying that it is inconsistent, globally, so you must see the whole.
You also maintain that "and when we try to our perception is always lacking detail." perhaps suggesting that when we see the whole, we lack the detail to see the inconsistency. Perhaps so, but even then, it is conceded I take it that the joining of the parts/sides A, B, C, is inconsistent, thus is can't be the case that globally they are consistent. Perhaps the quality or your experience is such that you literally do not perceive the inconsistency, even so, you could always deduce that it is inconsistent.
:)
A point on the comment by Anon 6 Sept: The paradigm contradiction is of the form A-and-not-A. But it could hardly be argued that this is "consistent in an important sense", on the grounds that each part, the A and the not-A, is by itself consistent. The contradiction comes precisely because the whole puts the parts together in a way that makes the parts contradict one another. Even the connective "and" plays a necessary role: contrast with A-or-not-A, which is not a contradiction. That is, with a different connective you abolish the inconsistency. To sum up, it is fallacious to argue: the parts are consistent, so the whole is.
ReplyDeleteI never argued that the parts are consistent, so the whole is. My point was that two adjacent sides are always going to be consistent. So you're always going to have local consistency but global inconsistency, with an impossible image.
ReplyDeleteI have no problem with impossible images. As long as you never say that we can hold a contradiction in our mind. For example, we conceive of an impossible image, and thereby conceive of a contradiction. When we conceive of an impossible image, our conception is always lacking the detail of where we would expect the contradiction to be.
"I have no problem with impossible images. As long as you never say that we can hold a contradiction in our mind."
ReplyDeleteIf you admit that the picture is globally inconsistent, then you must admit that the contradiction is literally "held" (represented) in our mind (at times). - Just stare at it.
"When we conceive of an impossible image, our conception is always lacking the detail of where we would expect the contradiction to be."
Yes - it is hard to say at what point some pictures become inconsistent (locally). But is that supposed to be an argument against the picture being inconsistent? (globally)
Consider the Sorites paradox as an analogy; it's hard to say at exactly what point of hair loss you call someone bald, or exactly how many grains of sand constitutes a heap, nevertheless, we do not infer that there are no bald men or heaps of sand.
Michael: why do you say that we never hold a contradiction in mind? This seems to fly in the face of the evidence herein that we do. Is it because you think that we never hold the whole of anything in mind, only its parts? This is precisely what gestalt psychology took pains to deny. Consider the consistent analog: look at a consistent triangle. Do we not hold the the whole of that triangle in mind? And if so, what is to stop us holding the whole of an inconsistent triangle in mind?
ReplyDeleteI am inclined to think that our conceptions are always lacking in detail when our conceptions are of something sufficiently complex. We can conceptualise a 2D triangle in its entirety because it is sufficiently simple. We can never conceptualise of an inconsistent image in our mind because 1) it is sufficiently complex, and 2) Because we (never or rarely) have anything more than a 2D mode of presentation.
ReplyDeleteWhen we conceptualise of an inconsistent image, we only have (say) one third of the image conceptualised at time t1, another third of the image at t2, and at t3 we have the other third of the image conceptualised, and we realise that what we conceptualised at t3 is inconsistent with what conceptualised together at t1 and t2.
I want to draw two morals from this:
1. That inconsistent images are indeed inconsistent.
2. We never conceptualise of any particular inconsistency in any particular inconsistent image.
I take 2 to have a common reason for why we can not conceptualise the following contradiction:
The cup is on the table and the cup is not on the table.
We can not conceptualise this proposition because there is simply nothing to conceptualise. Equally with inconsistent images, there are "parts" of the image which simply are not there.
"The cup is on the table and the cup is not on the table."
ReplyDeleteOne could simply reply that not all contradictions are true, such as the one above. And that the ones that we can conceptualise are the true contradictions.
I feel what the impossible picture senario endeavoring to convey and what is not stated, is the demension of time. Therefore the cup on the table or off the table is its proximity to being able to be corridinated by geometry!
ReplyDelete1" A line has a demension of one coordinant.A surface such as a plane or the surface of a cylinder or sphere has a demension of 2. The inside of a cube, a cylinder or a sphere is the three demension because three co-ordinates are needed to locate a point within these spaces."
If the three demensional object moves in different places- it has only move in the 4th demension, from one place to another.
Therefore an impossible picture is a construct of the three demension describe above, but the construct has been manipulated in the context of the 4th demension.
That is why the construct of an impossible picture presents diffuculties for logic to overcome.
I am not venturing anymore details on the subject.
Source 1: Wikipedia "Demensions"
Using time as a model for a fourth spatial dimension is certainly a useful idea, and has been considered by many geometers. However, it relies on our ability to think of time in a static, spatialised way. After all, the principal phenomenon to be accounted for is a wholly static, spatial image, and time is only an analogy for that.
ReplyDeleteHowever, mathematical analysis suggests that some of these images, particularly The Triangle, can exist in three spatial dimensions, just not three Euclidean dimensions, instead one of the dimensions is "rolled up".
Unfortunately, not all of these images are like that, particularly The Fork. I think that more than one cognitive mechanism is involved in these examples.
Another two cents worth!
ReplyDeleteIn reference to the construct of a impossible picture or an inconstient image. What I eluding too is that whilst constructing the picture or image it is formed in a sequence of time.
If I was to get a blank sheet of paper and just draw a straight line for example the right side of the fork example. And then stop. And a person glance over the sheet of paper all they would see is a line. They do not know that its the beginings of a inconstitent image. I then some days later draw the lines for the left side. Again the person now see's two lines. Some days later I fill in the rest too form the fork.
Now its an inconstitent image or an impossible picture at the time of its display to the interested person who first look at the first line.
Now at what time did the inconstient image appear? Was it when I drawed the first line or at the end when I filled in the middle. And say I decided to rub out the inconstiency. Lets for example say that the right line is A the left line is B the middle part of the image is C and we equate time as D
At A plus D, there is no inconsteint image.
At A plus, B plus, D, there is still no inconsteint image.
But at A plus, B plus, C plus, D plus, there is now an inconstient image.
D is always the constant, A,B,C are the variables, but all the variables need to be in place at the same time for an inconstient image to appear. Take away any of the A's, B's or C's from the inconstient image and you haven't got one!
Nevertheless its an interesting example of how our minds can construct impossiabilites! And interesting project for those to crack, but I stand by the constant of time in the construt of the image from a line to the end a inconsteint image.
The actual 2D images are always consistent, no contradictions, whether they are in parts or as a whole. However, what we perceive can be inconsistent. Our perception perceives the original 2D image as 3D, created an optical illusion, hence seems inconsistent and contradicts. If the images are perceived as they are, i.e. as 2D images with lines and shades, there won't be any contradictions. Therefore, it is not the 2D images that are inconsistent and incomplete, but our minds.
ReplyDeleteInconsistent images are not "optical illusions", as an "illusion" implies in some sense a tendency to believe falsely (eg. the Muller-Lyer illusion). There are no false beliefs in the case of the Triangle, etc., there just is no such triangle in the world.
ReplyDeleteNo-one is claiming that the 2D image is inconsistent. That would be absurd.
Many 2D images have a 3D content, eg. many paintings, photographs. The 3D content is in the mind. It is the 3D content that is contradictory. What this shows is that the mind is capable of representing inconsistent content.
But it isn't just a subjective matter. Consistent images with 3D content represent by means of perspective and occlusion, for example, and these are objective features of the world (which would appear in a photograph). The relation between 2D and its consistent 3D content can be described mathematically, for example by projective geometry. The relation between 2D and its inconsistent 3D content is analogous.
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ReplyDeleteHey! Your website is pretty awesome. I think you have a mistake on your page for Piranesi, though - in Plate VIII, the foot of the staircase is not flush against the face of the pillar. There's a statue between them, at least, symmetric with the one on the other side.
ReplyDeleteI have a drawing that I believe is an impossible image of a type I haven't seen before. Is there anywhere I could submit it for comment or review?
ReplyDeleteStuart, I tried an email reply which might have got through, I don't know. But in any case, there isn't any body which ratifies such things. But you can send it to us, say: Chris.Mortensen@adelaide.edu.au,
Deleteand we will look consider it for you. Others have done the same. I also suggest that you send it to your friends as a way of establishing priority.
Chris M
Thank you, Chris - I'll do this. Sorry the email didn't work - I'll write you directly to make sure.
ReplyDeleteMy definition of an impossible image is the fact that I can design and draw great furniture but I cant build it. Its impossible with my level of hands on skill! I designed a wine rack and believe it or not I couldn't build it. So i finally succumb to the pressure of just ordering one online from a site called www.wineracksite.com and now I just tell people I made it. Impossible image made real under the cold veneer of a white lie. Thoughts?
ReplyDeleteDear Anonymous
DeleteThanks for your comments. Impossibilia aren't just furniture, for example they can be buildings. One problem I see with your definition is this little word "can't" What we are after is things which are impossible and can't exist in our space, because they are in some sense incompatible with the laws of logic or mathematics: they can't exist not because the laws of nature prevent it, but because the laws of mathematics say they can't exist. Showing this rigorously is a difficult job!
Note also that things that look like the impossible triangle from certain angles can exist and indeed be built. What is impossible is for a thing to exist that has the properties that it seems to have.
Chris M
Hi there. I'm just reading Donald Hoffman's "Visual Intelligence" 1998, which led me to Reutersvald's "Devil's Triangle, which in turn led me to your site. I saw there the Ernst Stairs. When I looked at it, I thought the optical illusion wasn't - I thought the 2nd level (from bottom) had a bevel on the LH side. Hence easily made. On further examination I saw the "impossibility" trick - that it wasn't a bevel but an impossible construct
ReplyDeleteHi Chris, There's an impossible picture of another sort on your page "Piranesi's Carceri as Inconsistent" (I'm omitting the URL in order to avoid any automated filtering of comments.) The last image on the page is supposed to be to a file Prinasei-4b-3.jpg, but src attribute was accidentally set to a local machine file path, not a Web URL, so the picture is impossible to see.
ReplyDeleteThere are possible possibles,
ReplyDeleteThere are possible impossibles,and also
There impossible impossibles
BUCWAH
Top work fellas its good to see more Aussies doing this.