Number Cognition

The Ishango bone: Discovered in Congo, dates to ~22,000 years ago

Approximate Number System (ANS) Parallel individuation system

Symbolic number system

It represents large numerosities imprecisely

Represents small (less than or equal to 3 or 4) numbers of individual objects precisely (exact) It can track up to 3 or 4 separate individuals, and enables simple numerical computations Parallel means it can track multiple individual at once Individuation means individuate means make an individual out of or single out

Represents small or large numerosities precisely (like in word form)

Not really because he is just memorizing/mimicing what he has heard This does not mean they know what number means

A chimpanzee AI was trained to associate Arabic numerals (1-9) and content (dots, objects, etc.): the training took years Trained through reinforcement

Rat is in a cage with two levers, A and B. B delivers food but only after A has been pressed a fixed number of times. Rat was able to learn through trial and error and approximate the target number Not a matter of time: when rats were hungry, they pressed faster by were just as accurate

The greater the difference between the two numerosities, the more accurately the monkeys could order them Easier to distinguish bigger differences

Subjects see on the screen two Arabic digits and are asked to press a corresponding key to identify the larger one Speed and error rate negatively correlate with distance between the two digits More errors when the distance between digits is small

Simple differential sensitivity is inversely proportional to the size of the components of the difference; relative differential sensitivity remains the same regardless of size (depends on the ratio present) So basically the smaller the ratio, the faster you are at discriminating between the two sets and vice versa (the closer it moves to 1, the harder it is to discriminate)

Delta R = k * R

The idea is that the activation of one digit can activate other digits as well. For example, 4 can be strongly activated and activate numbers 3 or 5 approximately.

Saharan ants: fastest ants in the world Navigation: direction and distance (a vector) when looking for a food source Measure Direction: celestial compass Measure Distance: kind of like a Pedometer To test this: They manipulated the length of ants’ legs to see if it affects the distance they travel with stilts and stumps Findings: The ants with stilts overshoot their nest, and the ants with stumps undershoot their nest. Conclusion: Not sure how they do it. Maybe it is like a step counter or a probabilistic counter

Energy hypothesis Optic flow hypothesis Pedometer

Found in arthropods, track how much energy it took to get to the location to estimate travel distance Not applicable to ants: finding food takes less energy than carrying food home, yet they don’t undershoot return trip

Relying on optical flow Ex. visual cues Limited use: ants can find their home in the dark or with eyes covered

Counting the number of steps they took

They are linguistically special since many languages only have words for one, two, maybe three

Yes, Study: You show infants a puppet show with two outcomes: one where 1+1=2 and another where 1+1=1. You can tell the infants are aware because they are surprised when seeing the outcome of 1+1=1, and bored with 1+1=2 since they expect that.

Indigenous group in Brazil Limited number vocabulary Only has words for 1-5, and anything higher, there is no specific symbol/word

STUDY 1 Participants see a display of 1-15 dots in random order Asked to count how many dots were present Results were consistent with their limited vocabulary, with the numbers 1-5 using specific words for the numbers, but when they get past the larger numbers, they start to use the same word for all larger numbers

There are two possible answers It could be about culture (never needed to trade, thus doesn’t need to know numbers higher than 5) or language