Why does the brain make such erroneous assumptions?

[sprinkles]

Why does the brain make such erroneous assumptions?
Take for example the Necker Cube. Most people perceive this as a 3D cube, usually favoring one perspective of 3D, or flipping between two perspectives.

However, perceiving it as any kind of 3D is a mistake, because if it were meant to represent 3D, the back face would appear smaller, and the four horizontal edges would not be drawn as parallel. Yet, brains continue to perceive it as 3D even when they know this (like mine).

Why is this? Maybe the idealization of an object causes the brain to reject perspective illusions. Maybe the brain knows that when you look at a real 3D cube, the back face is not actually smaller, it just looks smaller. In fact this is what a 3D cube can look like in 3D programs that allow you to turn off perspective, but the brain seems to fail to recognize that seeing a 3D cube without perspective warping shouldn't be the case.

It's like the opposite of seeing a mirage. Your brain is convinced that it sees something, you can immediately recognize it as an illusion, but the illusion is actually present. There's really light bouncing to you from a place where it normally wouldn't, which is why you see it in the first place, and in the case of seeing objects such as a ship on the horizon, there actually is a ship somewhere and atmospheric effects are carrying the light from it further than usual. It's just not located where you're seeing it.

 

[sprinkles]

Also for comparison, this is what a 3D cube should look like.

There's some marks on this image which make it less ambiguous than normal. However, if one removes these marks, they'd not see it as an ambiguous cube. It could either be seen as an unambiguous cube, or something that is ambiguous but is not a cube.

 

[Flavus Aquila]

I suspect it is related to our ability to read imperfect letters, such as are found on security confirmation fields on web-sites, beyond the ability of machines to do so:

We easily communicate using imperfect symbols.


Looking at the first diagram, one can immediately interpret the lines as an attempt to represent a three dimensional cube - even if the proportions and angles be significantly out.

If, however, we are told that the image is carefully and deliberately drawn, there would be few who could not quickly come to interpret the image as possibly a representation of a distorted partial wedge; or simply an irregular two dimensional field of line/shapes. Most would also be able to state what information they would need to better understand such a diagram.


So, I think the most common first "lens" of interpretation we employ when looking at drawn figures is that of looking at such figures as an attempt to communicate.

 

[sprinkles]

I suspect it is related to our ability to read imperfect letters, such as are found on security confirmation fields on web-sites, beyond the ability of machines to do so:

We easily communicate using imperfect symbols.


Looking at the first diagram, one can immediately interpret the lines as an attempt to represent a three dimensional cube - even if the proportions and angles be significantly out.

If, however, we are told that the image is carefully and deliberately drawn, there would be few who could not quickly come to interpret the image as possibly a representation of a distorted partial wedge; or simply an irregular two dimensional field of line/shapes. Most would also be able to state what information they would need to better understand such a diagram.


So, I think the most common first "lens" of interpretation we employ when looking at drawn figures is that of looking at such figures as an attempt to communicate.

Interesting explanation.

However, letters are entirely conceptual. Cubes are not - a cube is also a concept, in that something which isn't an ideal cube isn't actually a cube. Of course truly ideal cubes are mostly theoretical since most structures have some error in them, so most cuboid objects only closely resemble a cube.

But, there is not truly an ideal letter, nor is there truly an ideal tree or an ideal smiley face, since the meaning of these do not depend on their precise geometric arrangements. i.e. you can draw a realistic tree and not have it be the same as another realistic tree. However if you draw a realistic cube it will be the same as other cubes if you align it in Euclidean space - the only thing that would differ would be scale.

 

[Flavus Aquila]

Interesting explanation.

However, letters are entirely conceptual. Cubes are not - a cube is also a concept, in that something which isn't an ideal cube isn't actually a cube. Of course truly ideal cubes are mostly theoretical since most structures have some error in them, so most cuboid objects only closely resemble a cube.

But, there is not truly an ideal letter, nor is there truly an ideal tree or an ideal smiley face, since the meaning of these do not depend on their precise geometric arrangements. i.e. you can draw a realistic tree and not have it be the same as another realistic tree. However if you draw a realistic cube it will be the same as other cubes if you align it in Euclidean space - the only thing that would differ would be scale.

I guess that gets into semiology.

Written words are different from pictorial representation; because words only convey parts of concepts, but as you note a picture can be used to refer to an ideal form, or a more complex concept... One picture being worth more than a thousand words and all that.

 

[just me]

Having turned the two cubes at different angles, one must actually TRY to look at their differences. Most folk know what someone meant to say, so they take it lightly. If it is abusive, they take harm with it. Where does the heart play into our understanding? Where does one gain the knowledge and understanding of what is ideal? Our minds can make a tree to be ideal or a letter to be ideal, it is all in the understanding of what "ideal" means to us. Take the O. That, to me, could be an ideal letter. Ask 1000 people to draw a tree and see what you get.

 

[sprinkles]

I guess that gets into semiology.

Written words are different from pictorial representation; because words only convey parts of concepts, but as you note a picture can be used to refer to an ideal form, or a more complex concept... One picture being worth more than a thousand words and all that.

Yes. Another interesting thing is how the world changes but ideas stay the same.

Take the kilogram for example. A long time ago when the kilogram was made a standard weight, governments defined the kilogram by precise master weights made out of durable metal. Copies of this master were sent to different countries to be stored in vaults in an attempt to always be able to know what a kilogram is.

The problem with that was that even these metals were not durable enough to resist the effects of time, and now these pieces of metal all have differing weights due to being stored in various geographic locations.

Which one is the real kilogram?

 

[Flavus Aquila]

Having turned the two cubes at different angles, one must actually TRY to look at their differences. Most folk know what someone meant to say, so they take it lightly. If it is abusive, they take harm with it. Where does the heart play into our understanding? Where does one gain the knowledge and understanding of what is ideal? Our minds can make a tree to be ideal or a letter to be ideal, it is all in the understanding of what "ideal" means to us. Take the O. That, to me, could be an ideal letter. Ask 1000 people to draw a tree and see what you get.

Each tree in nature is different. Nevertheless each tree is perfectly a tree.
There is only one possible proportion for a perfect cube.

Aristotle deals with this kind of stuff in his argument that humans have spiritual souls, It's to do with the ability to abstract from particulars to universals.

 

[just me]

I read Socrates, Plato, and the likes very cautiously. "Make haste cautiously." Augustus

 

[sprinkles]

Having turned the two cubes at different angles, one must actually TRY to look at their differences. Most folk know what someone meant to say, so they take it lightly. If it is abusive, they take harm with it. Where does the heart play into our understanding? Where does one gain the knowledge and understanding of what is ideal? Our minds can make a tree to be ideal or a letter to be ideal, it is all in the understanding of what "ideal" means to us. Take the O. That, to me, could be an ideal letter. Ask 1000 people to draw a tree and see what you get.

Well I don't mean ideal as in ideal beauty. I mean ideal as in archetypal ideal.

This is similar to the concept of the melting point of water ice vs what is an ideal temperature for you to be comfortable. Melting water ice happens at a specific temperature relative to atmospheric pressure. To know this ideal point for a given environment is to know the real temperature precisely, so it doesn't depend on feelings or opinions - it is objective.

However we usually don't deal with precise melting points, only approximate them.

(note that I say water ice to distinguish from other ice, such as dry ice, which is not water. So it sounds redundant, but it actually isn't.)

 

[Mary Shelley]

Perception knows only approximation.

 

[sprinkles]

Perception knows only approximation.

Shouldn't that be "Perception approximately knows approximation."?

I mean, in order to know that something is approximate, one has to idealize exactness. Approximate means "close, but not exact" so one must have a concept of "exact" in order to determine what it isn't.

 

[sprinkles]

Also I might add, my head a splode.

 

[barbad0s]

http://en.m.wikipedia.org/wiki/Set_(psychology)

 

[just me]

A Form is an objective "blueprint" of perfection.[SUP][19][/SUP] The Forms are perfect themselves because they are unchanging. For example, say we have a triangle drawn on a blackboard. A triangle is a polygon with 3 sides. The triangle as it is on the blackboard is far from perfect. However, it is only the intelligibility of the Form "triangle" that allows us to know the drawing on the chalkboard is a triangle, and the Form "triangle" is perfect and unchanging. It is exactly the same whenever anyone chooses to consider it; however, the time is that of the observer and not of the triangle. copied

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

 

[sprinkles]

A Form is an objective "blueprint" of perfection.[SUP][19][/SUP] The Forms are perfect themselves because they are unchanging. For example, say we have a triangle drawn on a blackboard. A triangle is a polygon with 3 sides. The triangle as it is on the blackboard is far from perfect. However, it is only the intelligibility of the Form "triangle" that allows us to know the drawing on the chalkboard is a triangle, and the Form "triangle" is perfect and unchanging. It is exactly the same whenever anyone chooses to consider it; however, the time is that of the observer and not of the triangle. copied

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

I reject the Theory of Forms, due to the recursive nature of properties, and properties themselves having properties.

For example, the unchanging nature of a triangle is different than the unchanging nature of a square. A triangle must have three sides and three angles, but the angles can vary. A square must have four sides and four angles, but the angles cannot vary.

If you take a triangle and change the angles, you might still end up with a triangle. If you take a square and change the angles, it is no longer a square.

 

[sprinkles]

Also if you think about it, for the Pythagorean theorem to work one needs unchanging squares. One determines the hypotenuse of right triangles using squares.

What about non-right triangles? You square it first with another triangle.

 

[Flavus Aquila]

A Form is an objective "blueprint" of perfection.[SUP][19][/SUP] The Forms are perfect themselves because they are unchanging. For example, say we have a triangle drawn on a blackboard. A triangle is a polygon with 3 sides. The triangle as it is on the blackboard is far from perfect. However, it is only the intelligibility of the Form "triangle" that allows us to know the drawing on the chalkboard is a triangle, and the Form "triangle" is perfect and unchanging. It is exactly the same whenever anyone chooses to consider it; however, the time is that of the observer and not of the triangle. copied

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

I reject the Theory of Forms, due to the recursive nature of properties, and properties themselves having properties.

For example, the unchanging nature of a triangle is different than the unchanging nature of a square. A triangle must have three sides and three angles, but the angles can vary. A square must have four sides and four angles, but the angles cannot vary.

If you take a triangle and change the angles, you might still end up with a triangle. If you take a square and change the angles, it is no longer a square.

If forms are considered to exist in themselves, in a Platonic sense, I also do not subscribe to the idea - with the exception of pure intellectual form: ie. angels, souls of the deceased.

If forms are considered as an integral aspect of material things, as in Aristotle's hylomorphic model, I subscribe.

If there is a 'form of triangle' it exists as a concept in an intellect.

 

[sprinkles]

If forms are considered to exist in themselves, in a Platonic sense, I also do not subscribe to the idea - with the exception of pure intellectual form: ie. angels, souls of the deceased.

If forms are considered as an integral aspect of material things, as in Aristotle's hylomorphic model, I subscribe.

If there is a 'form of triangle' it exists as a concept in an intellect.

Yes. However there is ideal form vs. realistic form vs. real form. Some times these are the same form. Other times they are not.

However reality is made of real forms, not ideal forms or even realistic ones. Ideal form being the theoretically perfect or accurate form - this idea exists in that we can conceive of it and compare to it (if it did not we'd never realize when something isn't perfect). Realistic form being what could be real in existing conditions - e.g. you can build one of it if you haven't already. Real form is what is actually there, and how it actually is, outside of your perceptions.

 

[Flavus Aquila]

Yes. However there is ideal form vs. realistic form vs. real form. Some times these are the same form. Other times they are not.

However reality is made of real forms, not ideal forms or even realistic ones. Ideal form being the theoretically perfect or accurate form - this idea exists in that we can conceive of it and compare to it (if it did not we'd never realize when something isn't perfect). Realistic form being what could be real in existing conditions - e.g. you can build one of it if you haven't already. Real form is what is actually there, and how it actually is, outside of your perceptions.

There are triangles within a circle, however, a circle is not defined by triangles. Concretely I would say that there are potentially triangles in a circle, but not formally.

The notion/form of a triangle within a circle is an abstract - litterally abstracted by the intellect, from material relations. This abstract can then be imposed on matter, by for example, drawing a triangle within a circle. However, this drawing will only be an imperfect representation of a perfect, abstracted intellectual form of triangle.

I don't like the term "ideal form" because of it's platonic associations, as though there were really such a thing as triangle-ness outside the intellectual notion of what a triangle is.

The intellectual notion of a triangle is universal, insofar as it comprehends all three sided, three angled closed figures/shapes/spatial-relationships. It is not ideal, so much as abstracted from all particular material examples.