COGS - Automatic Magnitude Representation.docx

Automatic Magnitude Representation Weber Ratios Cardinal Principle Knower Bootstrapping (Linking of things to existing concepts and expansion of existing concepts) Conceptual Development What is real world knowledge and how do you acquire it Number Cognition – How do we acquire the knowledge for nu...

Automatic Magnitude Representation Weber Ratios Cardinal Principle Knower Bootstrapping (Linking of things to existing concepts and expansion of existing concepts) Conceptual Development What is real world knowledge and how do you acquire it Number Cognition – How do we acquire the knowledge for numbers and quantities Number and Quantity Analog Magnitude Representation Prallel individualation Are numbers hard wired Paper + Presentation One traditional view: We need formal training Number is a part of formal system and we must learn this explicitly Jean Piaget Psychologist focused on child development’ Piaget Conservation Tasks Given two rows of quarters, if you were to space out one row of quarters, the child may believe that the more spaced out row is larger Changing the size of different objects, such as pouring equal amt of water in a small glass into a taller glass, will trick the child into believing that the water in the tall glass is more We seem to require some level of guidance in comparing quantities BUT We can do some reasoning from infant hood A Xu and Spelke 2000 study showed infants pictures of 8 dots and they are then shown 16 dots Babies look longer at the 16 dot pictures This has a different quantity and amount Paper: The Representations Underlying Infants Choice of More Find out if infants represent a quantity as a number or an analogue magnitude The paper found that in the first of experiment, infants would chose larger quantities when given 1 or 3 cookies The infants would not choose a box with 4 cookies as opposed to a box with 2 as consistently Analog Magnitude Representation: How we understand number and magnitude We have a hardwired sense of magnitude We learn to map abstract quanties to numbers as we grow up Analog magnitude representation is about proportion We use Webers Law to quantify A measure of discriminability that works for all kinds of perceptual quantities $\frac{\mathbf{\mathrm{\Delta}I}}{\mathbf{I}}\mathbf{= K}$ Our ability to discriminate improves with age (K is our ability to discriminate) Rats also improve with analog magnitude representations. Parallel individuation of small sets Relies on MULTIPLE OBJECT TRACKING Multiple object tracking is something we have to do in the real world In the same Paper: Abstract Parallel individualation of small sets: Infants have pre existing slots that they use to compare magnitude They put each object in a group, for example a group of three, into a box One cracker goes to tone box If there are too many crackers for pre existing slots This is something that develops overtime and is not connected in any way to Weber Ratios Number is implicitly represented and bound to individual objects System is separate from AMR and not connected to Weber Ratios Core system provide limited number representation Parallel individuation of small sets provides basis for first few numerals One is mapped to sets of 1 Two mapped to sets of 2 ETC You gain the ability to map larger numbers Bootstrapping involves realizing that three from the counting routine is the same word as three for the set of three Sometimes this is called Quinian Bootstrapping Process Using mapping, you become a One knower all the way to four knower THEN you become a Cardinal Principle Knower (Can generalize after four) The cardinality principle refers to the understanding that the last count word in the counting sequence represents the total number of items in the collection The word five is learned in a different way than the word four Infants will only recognize numbers that are higher than their known numbers as quantities that are much larger than what they know. Thus, if you ask them to hand you a number of items above that of what they know, they will become confused. They will often hand you large numbers of the same object