Seeing numbers Perception R.W. Oldford University of Waterloo
What is in a number? Properties Some possible properties a number might have are ◮ a visual representation ◮ a picture encoding a value which can be decoded ◮ easily, efficiently, accurately (both encoding and decoding) ◮ unique identity (can tell when we see the same number again; distinguish between numbers) ◮ comparable, having quantity, size, or extent ◮ numbers can be (at least partially?) ordered by size, i.e. ranked ◮ has magnitude: quantity, size, extent ◮ cardinality, how many? (identify and count; e.g. how many are red?) ◮ difference in values have meaning (interval-scale; e.g. temperature) ◮ ratio of values is in turn a meaningful number (ratio scale; e.g. height)
Identity Discrimination Both QR codes and UPC-A bar codes satisfy identity – can visually discriminate one number from another . Exercise: what are the four numbers?
Identity Discrimination This is all we need, if the data we are looking at are categorical. For example: ◮ coin toss: heads, tails ◮ state of health: well, ill, dead ◮ mammal species: baboon, rat, dog, human, humpback whale, gorilla, . . . ◮ sex: male, female ◮ colour: red, orange, yellow, green, blue, violet ◮ person: Justin, Ameer, Ana, Chris, Andrew, Xiaoqing, Karan, Jacob, Kayla, Kofi, Matt, . . . Any set of distinguishable visual representations will do, but some will be better than others .
Identity Visual representations - Letters, simple stick shapes Simple line combinations as used in block letters, etc. can be useful, provided the stick shapes are easily distinguished. For example, what distinctions appear here?
Identity Visual representations - Letters, simple stick shapes Simple line combinations as used in block letters, etc. can be useful, provided the stick shapes are easily distinguished. For example, what distinctions appear here? Angle (or orientation), spatial location, letter value (T or L). How many Ls are there? 1? 2? 3? 4? 5? 6? 7? It is kind of hard to distinguish the Ls from the Ts here; this might have been easier if orientation was not changing at the same time.
Identity Visual representations - Shapes Simple geometric shapes can also be distinguished. For example, how many different shapes are here? What distinctions are being made?
Identity Visual representations - Shapes Simple geometric shapes can also be distinguished. For example, how many different shapes are here? What distinctions are being made? How many different shapes? 5? 6? 7? 8? 9? 10? 11? 12? 13? 14? What distinctions are being made? Shape, location, orientation, size, reflection. Questions ◮ Might regular shapes be more easily recognized? ◮ More easily distinguished? ◮ Is shape invariant to orientation? size? reflection?
Identity Visual representations - visual location An often overlooked means of discriminating categories is simply spatial location ◮ points in the same category are grouped spatially (close to each other) ◮ categories are separated spatially (more space between than within categories) ◮ add a boundary (here a rectangle) to enclose each group Works well with few categories.
Identity Visual representations - Names Simple labels provide a large range of different values that are relatively easily distinguished.
Identity Visual representations - Names Simple labels provide a large range of different values that are relatively easily distinguished. How many categories are here? How many labels in each category?
Identity Visual representations - Names Simple labels provide a large range of different values that are relatively easily distinguished. How many categories are here? How many labels in each category? red? green? blue? Note that in some cases, such as colour name, the colour of the label could induce confusion rather than further separation.
Identity Visual representation - thinking outside of the box We are very good at distinguishing faces: We can even recognize familiar faces and distinguish these from unfamiliar faces. We might use a different face for every category.
Identity Visual representation - faces It is important to our survival that we have evolved the ability to recognize faces (e.g. predators, family, friend, and foe) and even to distinguish facial expressions (e.g. to understand social situations). Facial recognition occurs very quickly within a particular region of the brain. Moreover, there are neurons in our brain that fire much more frequently whenever we see a face. Here the firing rate of the neuron is much higher when presented with something that looks like a face.
Identity Visual representations - faces Can easily recognize familiar faces. For example, who is this?
Identity Visual representations - faces Can even recognize faces, as faces, when upside down!
Identity Visual representations - faces Can recognize faces when the orientation changes!
Identity Visual representations - faces Can recognize faces when the orientation changes!
Identity Visual representations - faces Can recognize faces when the orientation changes!
Identity Visual representations - faces Can recognize faces when the orientation changes!
Identity Visual representations - faces Can recognize faces when the orientation changes! · · · um, wait a second?
Identity Visual representations - faces · · · huh?
Identity Visual representations - faces · · · huh?
Identity Visual representations - faces · · · huh?
Identity Visual representations - faces · · · whaaa . . . ?
Identity Visual representations - faces · · · whaaa . . . ?
Identity Visual representations - faces · · · whaaa . . . ?
Identity Visual representations - faces · · · OK, that’s messed up! What happened?
Identity Visual representations - faces These are identical images! We focus on different features, with different priorities, as determined largely by our evolutionary path and cultural training. What we “see” is a mental construction . . .
Identity Visual representation - faces The importance of faces along our evolutionary path unfortunately means we see them everywhere, even where they are not – we construct what we see! Face on Mars Grilled cheese sandwich sold on EBay
Identity Visual representations - colour The human visual system also distinguishes COLOUR . The human retina contains about 6 million colour photoreceptors called “ cones ”, and about 120 million photoreceptors called “ rods ” Human eye Human retina and photo receptors Distribution of receptors So let’s try it.
Identity Visual representations - categories from hues The safest colour use for identifying categories is having each category be coloured with a different hue: Even here there can be some challenges distinguishing hues that are close to one another. These work best when there are few categories so that hues can be chosen that are widely separated.
Identity Visual representations - colour And then there is the problem of colour blindness ( ≈ 1 in 12 men, 1 in 200 women). A number A number A path
Identity Visual representations - colour Rods: ◮ about 120 million rods in the human retina ◮ rods are distributed more evenly throughout our retina ◮ extremely light sensitive (a single rod can detect a single photon) ◮ do not detect colour (achromatic); instead register differences in light and dark ◮ provide most of our night vision (hence black and white at night) Cones: ◮ about 6 million cones in the human retina ◮ concentrate near the fovea (focal point) in our eye ◮ 3 different types of cone distinguishing three different sets of electromagnetic wavelengths (roughly corresponding to red, green, and blue) ◮ together they allow us to distinguish colours (much like an RGB display is able to produce the same)
Identity Visual representations - colour Cones: 3 different cone types react more to different wavelengths of light (short, medium, and long roughly corresponding to blue, green, and red) Differences in the signal strength from the cones being stimulated help us perceive different colours. (Note that red sensitivity was the last to evolve.) Wavelength sensitivity of three cone types (source Lotto et al (2011) Optics & Laser Tech. )
Identity Visual representations - colour Deficiency in each colour (either cone, or pathway from cone): 1. Protanopia – deficiency in perceiving ‘red’ light 2. Deuteranopia – deficiency in perceiving ‘green’ light 3. Tritanopia – deficiency in perceiving ‘blue’ light. Following images are from www.colourblindawareness.org Normal Vision Protanopia – red deficiency Some care needs to be taken so that any visualization produced will also be accessible to the colour blind www.color-blindness.com/coblis-color-blindness-simulator.
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