Lecture 6- Numbers and the brain Flashcards
What was the lever experiment in rats to test their numeracy skills?
- present rats with two levers, A and B -lever B gives them a food reward but only after they have pressed A a set number of times
- rats work out the rules by trial and error
- while they improve with practice, they never become very accurate
- rats tended to press on average the right number of times, but with a degree of imprecision
- rats get worse as you increase the number required (look at the 16 graph)
What are rats’ counting abilities?
-the higher the number required the greater the degree of imprecision -rat counting is analogue not digital (it is about 4 but don’t think of it as a digit) -they cannot count abstractly (the horn and light flashing cannot combine) -can be taught to push the lever if a light flashed twice or a horn sounds twice
What are the abilities of other animals?
-other animals show similar capacity -raccoons can discriminate 3 grapes from 2 or 4 -birds can peck every 5th seed -pigeons can estimate 45 pecks as different from 50 pecks
What is counting like in primates?
-chimpanzees understand fractions -a half an apple is more like a half a glass of milk than it is like a full glass -a quarter apple plus a half glass of milk is more like 3/4 circle than it is like a full circle
What is the distance effect in chimpanzees?
- a chimp will choose the tray on the left over that on the right
- it identifies 4+3 as being more chocolate than 5+1
- works best for large differences but much worse for small differences (only 70% correct for difference of 1= hardly better than chance)
What is the magnitude effect in chimpanzees?
-for the same difference(distance), a chimp has more trouble working out which is bigger if both numbers are large -2 and 3 easier to decide about than 6 and 7 -animals are good at 1,2 and 3 but larger numbers more imprecisely imagined =analogue not digital!
What are the numeracy skills of animals? (summary)
-animal brains have fuzzy number estimators (the approximate number system) -only chimps have shown crude symbolic calculation -many animals can recognise, memorise and compare numerical quantities -some can crudely add them -all show the distance and magnitude effects
Can babies count?
-babies can appreciate that 1+1 is not 1 and 2-1 is not 2(the mickey mouse doll test) -with the chocolates choose row with more -can handle numbers up to 4 but get confused after that -still do it if object changes shape (only numerosity counts) -no ordinal competence (3>2), just different -same approximate number system as animals
How long does it take to estimate the number of objects present? (adults)
-normal people estimate small numbers (1,2,3) much faster and with much less error than number larger than 3 -magnitude effect
What is the response time curve in adults?
- 1 and 2 are identified faster than 3, but 4 is disproportionately longer again
- error rate really increases from 4 on
- up to 3 objects number is determined without counting
- beyond 3, higher error rate requires counting
- this is only numerosity not mathematics
How do humans perform in comparing numbers?
-adult humans show both the distance and magnitude effect -ask “which is bigger?”: faster at comparing 1 and 9 than 41 and 49(magnitude effect) -faster at comparing 41 and 49 than 41 and 42 (distance effect) -when compare all numbers between 31 and 99 with 65, become slower as approach 65, 64 and 66 the slowest
What is the number line analogy?
-animals, babies and adult humans compare numbers as if they are strung out across physical space and more crowded in the higher regions -the distance effect and magnitude effects can be easily explained in this analogy -it is as if this lines is in your mental space -anything that is highe rnumber= more squashed later -this is an analogy, not reality -some people actually imagine the line in their mind in west= left to right, arabs= right to left
What did the fMRI study reveal about the number line?
- showed clusters of objects
- mapped BOLD signals that responded to differences in number
- identified region in superior parietal cortex that was topographically organised for numerosity
- graph of the bold response= response to blood flow
- the BOLD signal went up as the number of objects incrased to 2 and 3 then decrease
- hot spot in cortex that is interested in clusters of 2 or 3 objects
Where is the number line in the brain?
- superior parietal cortex
- bilateral sense of numerosity
- in both hemispheres
- low numbers in hot colours, high in cold colours
- this is the number line
- actually in neurons
What is unusual about the topography of numerosity?
-many sensory functions are topographically organised (hearing, vision, somatosensory) -this is the first topographic organisation found of a cognitive function -is this the neural equivalent of the number line?i=t looks like it -but mayne a coincidence -fuzzy number estimator is the superior parietal cortex
What is numerosity?
-an intrinsic property of many animal brains -basic number comparisons -extremely basic -not precise
Is mathematics uniquely human?
-yes -has precision
What is the hypothesis about why humans have mathematics?
-language gives an accurate number ability= mathematical manipulation uses linguistic pathways -mathematics is an example of something we do with language -it is a way of language -if that is the case, then no words for numbers shouldn’t have maths -are they only left with numerosity???
Test of language/maths hypothesis 1: What happens if you have no words for numbers?
-Mandurukú of Amazob jungle only have words for 1-5 -large numbers are approximated (more than one hand, some toes, more than all the fingers of both hands and then some) -could pick more numerous of the two sets of 20 to 80 dots -could add and compare approximate numbers -could not subtract numbers larger than 5 even when the result was less than 5 ===have only an approximate number system -if you don’t have the language don’t have mathematics
Test of language/maths hypothesis 2: Split brain patients?
-left (language) hemisphere should have significant mathematical ability, right only approximate number system -test on split brian patient -present a mathematical problem, show possible answer to one or the other hemisphere -Left hemisphere: near 100% for addition, subtraction, division and multiplication -Right hemisphere: above chance for subtraction and addition (when differences large), at chance for multiplication and division
What are the left and right hemisphere mathematic abilities?
-mathematical ability is a left hemisphere ability
What are lesion studies good for in research of mathematical ability?
-where are the maths centres in the brain -strokes are revealing about how the number sense is organised -possible to destroy or disconnect very specific aspects of maths ability
What lesions result in number problems?
-lesion in area of left inferior parietal cortex -causing acalculia (inability to calculate)
What are the symptoms of a left inferior parietal cortex lesion patient?
-can convert 6 in words -comparison compromised (2 lies between 3 and 5) -subtraction and multiplication sometimes split (can subtract but not multiply and vice versa) -worst for abstract arithmetic, can manipulate it if put into discrete things (like time 7 is 2 hours before 9)
