Lecture 6- Numbers and the brain Flashcards

1
Q

What was the lever experiment in rats to test their numeracy skills?

A
  • 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)
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2
Q

What are rats’ counting abilities?

A

-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

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3
Q

What are the abilities of other animals?

A

-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

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4
Q

What is counting like in primates?

A

-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

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5
Q

What is the distance effect in chimpanzees?

A
  • 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)
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6
Q

What is the magnitude effect in chimpanzees?

A

-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!

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7
Q

What are the numeracy skills of animals? (summary)

A

-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

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8
Q

Can babies count?

A

-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

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9
Q

How long does it take to estimate the number of objects present? (adults)

A

-normal people estimate small numbers (1,2,3) much faster and with much less error than number larger than 3 -magnitude effect

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10
Q

What is the response time curve in adults?

A
  • 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
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11
Q

How do humans perform in comparing numbers?

A

-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

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12
Q

What is the number line analogy?

A

-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

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13
Q

What did the fMRI study reveal about the number line?

A
  • 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
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14
Q

Where is the number line in the brain?

A
  • 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
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15
Q

What is unusual about the topography of numerosity?

A

-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

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16
Q

What is numerosity?

A

-an intrinsic property of many animal brains -basic number comparisons -extremely basic -not precise

17
Q

Is mathematics uniquely human?

A

-yes -has precision

18
Q

What is the hypothesis about why humans have mathematics?

A

-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???

19
Q

Test of language/maths hypothesis 1: What happens if you have no words for numbers?

A

-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

20
Q

Test of language/maths hypothesis 2: Split brain patients?

A

-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

21
Q

What are the left and right hemisphere mathematic abilities?

A

-mathematical ability is a left hemisphere ability

22
Q

What are lesion studies good for in research of mathematical ability?

A

-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

23
Q

What lesions result in number problems?

A

-lesion in area of left inferior parietal cortex -causing acalculia (inability to calculate)

24
Q

What are the symptoms of a left inferior parietal cortex lesion patient?

A

-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)

25
Q

What is Gerstmann’s syndrome?

A

-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

26
Q

What three areas of the brain were identified as active during numerical tasks by fMRI and PET studies?

A
  1. Horizontal inferior parietal sulcus 2. Angular gyrus 3. Posterior superior parietal lobe
27
Q

What does horizontal inferior parietal sulcus do?

A
  • operations that call upon quantitative representation of numbers
  • bilateral
  • location of the number line? (this study prior to the other)
  • active in subtraction
28
Q

What does angular gyrus do?

A
  • 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)
29
Q

What does posterior superior parietal lobe do?

A
  • operations that call upon a range of number tasks but also attention and orientation in space
  • bilateral
  • largely speculative
30
Q

What does loss of angular gyrus lead to?

A

-loss of multiplication due to affect in language(times table are rote learnt= a language task)

31
Q

What do you need inferior parietal sulcus for? (horizontal)

A

-for subtraction -number line needed to manipulate numbers

32
Q

What is posterior superior parietal needed for?

A

-to attend to appropriate part of the number line?

33
Q

What other areas may be important in mathematical ability?

A

-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)

34
Q

Is the ability to attend to numerosity and manipulating it internally present in all animals?

A

-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