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)
What is Gerstmann’s syndrome?
-lesion in left inferior parietal cortex lead to it -present with: acalculia, writing problems, distinguishing left and right (how you direct attention to space= that is why problem distinguishing left and right), distinguishing fingers -inferior parietal lobe is at intersection of language, visual attention and numerical representation networks
What three areas of the brain were identified as active during numerical tasks by fMRI and PET studies?
- Horizontal inferior parietal sulcus 2. Angular gyrus 3. Posterior superior parietal lobe
What does horizontal inferior parietal sulcus do?
- operations that call upon quantitative representation of numbers
- bilateral
- location of the number line? (this study prior to the other)
- active in subtraction
What does angular gyrus do?
- operations that call upon an exact manipulation of numbers
- verbal number manipulations(mathematics)
- predominantly on left side
- active in multiplication (only left hemisphere structure)
- if verbal manipulation or written, then have trouble if don’t have the region and cannot do multiplication if don’t have it)
What does posterior superior parietal lobe do?
- operations that call upon a range of number tasks but also attention and orientation in space
- bilateral
- largely speculative
What does loss of angular gyrus lead to?
-loss of multiplication due to affect in language(times table are rote learnt= a language task)
What do you need inferior parietal sulcus for? (horizontal)
-for subtraction -number line needed to manipulate numbers
What is posterior superior parietal needed for?
-to attend to appropriate part of the number line?
What other areas may be important in mathematical ability?
-frontal cortex is also activated when inferior parietal cortex is active -may be holding number in memory? (the ones on the slide above are the gateways but there may be many more areas that are involved - if comparing any two numbers= frontal cortex is also activated IPC= inferior parietal cortex)
Is the ability to attend to numerosity and manipulating it internally present in all animals?
-yes -even in babies without training or language skills -it involves at least in part specialised regions of the brain -accurate manipulation of larger numbers is a learnt, language dependent ability
