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We know the Kanizsa Triangle.

enter image description here
Kanizsa Triangle

I was socialized in a "western" world, where I learned mathematics for about 13 years; I have designed products surrounding me using geometric forms and so forth.

I wonder if somebody would see the triangle who never or rarely saw a triangle before?

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It's a difficult question to answer. My educated guess is that the appearance of the triangle, and illusionary contours in general, would persist, even in individuals who have never seen a triangle before in their lives. I think they would perceive the illusionary contours, but it might just not make sense to them, as the shapes may be unfamilair to them. In other words, they would not associate the form with something meaningful. The reason why I expect previous experience with geometrical shapes is unimportant for illusiuonary contours to be perceived is two-fold:

  1. Illusionary contours are generated in the secondary visual cortex (V2), which is a low-level part of the visual system. It performs relatively simple processing such as the coding of orientations, contours and the perception of background and foreground (Anzai et al., 2007). Such low-level processing is, expectedly, largely innate.
  2. The neural representations of illusionary contours have been shown in a variety of species. Admittedly, most electrophysiological evidence comes from primates (e.g., Heydt, 1984), but illusionary contours have even been shown to be recognized by cuttlefish (Zylinsk et al., 2012). Hence, given the fact that relatively uncomplicated species like cuttlefish are able to successfully perceive illusionary contours, I doubt that prior experience in the geometry of the illusionary contour is a critical factor in perceiving it.

References
- Anzal et al., Nature Neurosci (2007); 10: 1313 - 21
- Heydt, Science (1984); 224(4654): 1260-2
- Zylinsk et al., Proc Biol Sci (2012); 279(1737): 2386–90

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First, in the context of your reference to cultural context, one aspect of your question appears to be whether or not a person who has never had experiences of triangles before can have a triangle experience. Second, it is of interest whether that experience can be brought about by a configuration of shapes which is considered appropriate to elicit the perception of illusory contour.

As to the second question, you seem readily inclined to take the view that someone who has previously seen triangles, knows what triangles are, and can also verbally express that experience (»I'm seeing a triangle!«), can indeed have a triangle experience when looking at the Kanizsa figure. (This is not to be taken for granted. Taking a gestaltist view however will grant that perception at least some kind of actual reality. Consider the question whether you see a second triangle constituted by black lines behind the ›illusory‹ one.)

Now, if we are willing to allow this, then we can actually reduce the whole question to the first part. A common psychological stance on perception, taking input from philosophy of mind, assumes a perceptual episode to be constituted by an object providing stimulation to the senses, leading to a ›perception‹ that is not conscious, which is then somehow translated into a conscious perception that corresponds to a phenomenon, which again is fully recognized in the sense of a perceptual judgement. Here, of particular interest is the difference between perceptual experience and perceptual judgement (you might also ask yourself whether a cat can see a triangle):

[W]e must be careful to distinguish such a perceptual judgement from a perceptual experience. A person may have a perceptual experience of seeing a table to be rectangular without necessarily being willing, or even able, to form the perceptual judgement that he sees that a certain table is rectangular. […] [T]he person may be unable to form the perceptual judgement in question because he lacks the requisite concepts. Thus, for example, one might be prepared to attribute a young child a perceptual experience of seeing a table to be rectangular and yet doubt whether the child is capable of forming the perceptual judgement that it sees that a certain table is rectangular […]. (Lowe 2000, pp. 132–133)

Summing it up, the answer is yes, that person could justifiably be said to see a triangle, however, depending on particulars of the question, the answer might differ.

Taking a different approach, we can take the question to mean: Given which previous experience are we capable to perceive illusory contour?, and there is evidence that the visual system's capability to recognize simple shapes is largely innate (notwithstanding the fact that lack of any visual input will prevent vision to develop in the first place). See Christiaans answer for some more detail. A particularly interesting question in this context, which relates to the difference between perceptual experience and perceptual judgement discussed above, is at what age is a person capable of perceiving illusory countours? In this regard, Ghim (1990) concludes that »infants as young as 3 months of age are able to perceive subjective contours«, and in a related study, Curran et al. (1999) conclude that »by 2 months of age, the infant's visual system contains the nonlinear mechanisms necessary to extract an illusory contour from aligned terminators«.


References:

  • W Curran, OJ Braddick, J Atkinson, J Wattam-Bell, R Andrew. 1999. Development of illusory-contour perception in infants. Perception, Vol. 28, pp. 527–538.
  • H-R Ghim. 1990. Evidence for perceptual organization in infants: Perception of subjective contours by young infants. Infant Behavior and Development 13(2), pp. 221–248.
  • EJ Lowe. 2000. An Introduction to the Philosophy of Mind. Cambridge University Press.
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I think that illusory contours could be experienced independently of cultural influence: a person would see a figure but she would not know it is a "triangle". The reason is that illusory contours as the ones you see in the figure share many of their properties with illusory phenomena that could be obtained with simple alignments of image features. As such, the illusion of a contour can be obtained also with overall irregular shape, although the regularity of the figure could facilitate the occurrence. There are several examples of irregular figures with illusory contours. See for the phenomenon of neon color spreading. Displays in this case easily allow more complex patterns, see for example:http://www.blelb.ch/oldblelbsite/english/blelbspots/spot05/expspot05_en.htm

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