Math on the Brain?

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Math on the Brain?

Postby vivian maxine on May 16th, 2016, 10:29 am 

https://www.sciencedaily.com/releases/2 ... ce+News%29

Scientists have found a mathematics network on the brain that is totally separate from the language regions. The question is can we have thought without language. The tests were only four seconds and I wondered how much you can test in just four seconds. But I suppose, with math, you could. It's a great story.
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Re: Math on the Brain?

Postby dandelion on May 16th, 2016, 11:39 am 

That looks really interesting, thanks.

http://www.unicog.org/publications/Amal ... s%20SI.pdf

Abstract
The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit.
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Re: Math on the Brain?

Postby Natural ChemE on May 16th, 2016, 4:59 pm 

vivian maxine,

Neat study! Though I have to admit that I was unaware that the idea of thought-without-words was considered an open question. At least personally, I don't use words at all in the great majority of my thought processes; figuring out how to express what I'm thinking in English takes a lot of conscious effort.
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Re: Math on the Brain?

Postby vivian maxine on May 16th, 2016, 5:54 pm 

Natural ChemE » May 16th, 2016, 3:59 pm wrote:vivian maxine,

Neat study! Though I have to admit that I was unaware that the idea of thought-without-words was considered an open question. At least personally, I don't use words at all in the great majority of my thought processes; figuring out how to express what I'm thinking in English takes a lot of conscious effort.


I did some testing this afternoon. A simple problem - changing grams to teaspoonsful. I have to admit that I did use words as I first rounded off the number and then divided. I do wonder, though, if how we do it has anything to do with how we were taught. Our arithmetic (not math) was totally rote. Not much comprehension to it beyond the simple add and subtract. And no advanced math at all. Not the kind where you'd have to picture what is happening. One year of algebra and one year of geometry and that was it.

Now I am sitting here thinking. I don't have to do that with foreign languages. We learned languages the conversational way and it just comes natural to me to think the right word or right sentence. No analyzing at all.

Of course that study found those math regions even before the child started school. That is different; yet something to think about.

Truly is an interesting study, isn't it?
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Re: Math on the Brain?

Postby Eclogite on May 18th, 2016, 5:16 am 

Natural ChemE » Mon May 16, 2016 8:59 pm wrote:vivian maxine,

Neat study! Though I have to admit that I was unaware that the idea of thought-without-words was considered an open question. At least personally, I don't use words at all in the great majority of my thought processes; figuring out how to express what I'm thinking in English takes a lot of conscious effort.
I shared your puzzlement at the notion that thought-without-words was in some way controversial.

While many, perhaps a majority, of my thoughts may begin with words, many of them begin (and some continue) as visual explorations. For example, if someone says to me that there is a large Asian population in Leeds-Bradford I see in rapid sequence a map of England with Leeds-Bradford highlighted, a thoroughfare in the city crowded with ethnic shops, a map of the Indian sub-continent, a news item speaking of racial tensions, etc. Total elapsed time no more than two and a half seconds, but not a word in sight (or sound).

In a more structured example I may envisage an incident of equipment failure, not in words, but visually. I then need to convert that visual understanding into words in order to communicate it.

My expectation is that most (all) people think this way, since words are so painfully slow.
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Re: Math on the Brain?

Postby jocular on May 18th, 2016, 6:02 am 

In the past few days I have been trying to visualize places in my mind ** (it is an exercise designed to improve this kind of facility).

What I have discovered (in my case) is that it is (so far) quite impossible to recall visually any location that I do not associate with a particular event.

Any visual recall has to be "tagged" somehow. So I doubt visual recall exists in a standalone way from some kind of an analysis.

I know people are capable of drawing fantastically detailed visual scenes from memory. Perhaps their brains have different hardware to mine because I doubt I can train mine(in a standalone way).

** EDIT: not "places in my mind" ,obviously
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Re: Math on the Brain?

Postby vivian maxine on May 18th, 2016, 7:07 am 

Aren't we really just saying that different people envision and think differently, perhaps based on their own talents, their learned methods and - to a great extent - habits of their daily activities?
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Re: Math on the Brain?

Postby jocular on May 18th, 2016, 7:39 am 

There are differences between people and the way an individual can develop his or her abilities in a new direction but I would have thought it is also an important consideration to understand the underlying connections between the different capabilities of thought processes.

This study finds (unsurprisingly perhaps) that language skills and mechanical skills are "segregated" into different areas of the brain.

I would ask the question "what might be the connection between these two areas? " We don't have two brains after all so they must be "talking " to each other.

What is the common language ? Did social language develop anciently from basic mathematical calculations ?

Or did both develop from the same "evolutionary parent" and what might that parent be?
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Re: Math on the Brain?

Postby Dave_Oblad on May 18th, 2016, 7:21 pm 

Hi all,

Obviously, we don't think in words as they are too slow (mentioned above). When I play a sport, I don't think in words, I think in motion simulations. When I write a program, I think in visualizations of information movement. I only think in words when I need to formalize something, like practicing what I will say to someone soon.

Here is an observation I'd like some feedback on. Most of the Dreams I have use no words. I can't even recall ever having a conversation in a dream. Most of my dreams involve situations I'm trying to resolve.. like finding my car in a parking lot. (I hate that dream as it's rather frequent.) How frequently do you dream using words in your dream?

Best wishes,
Dave :^)
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Re: Math on the Brain?

Postby BurtJordaan on May 19th, 2016, 1:31 am 

Dave_Oblad » 19 May 2016, 01:21 wrote:Here is an observation I'd like some feedback on. Most of the Dreams I have use no words. I can't even recall ever having a conversation in a dream. Most of my dreams involve situations I'm trying to resolve.. like finding my car in a parking lot. (I hate that dream as it's rather frequent.) How frequently do you dream using words in your dream?


I have similar recollections - no verbals in dreams that I'm aware of. I also noticed patterns in the dreams that I remember. When I'm doing frequent mathematical work, I have a recurring 'situational' dream that involves finding my way (on foot) through a difficult, partially known path, either roads or through buildings. I mostly wake up when I find myself at a dead end or with the only option ahead rather precarious. Of course one remember those where you wake up in such a situation more vividly.

I relate this to the subconscious 'working' on the math problem, at least trying to organize the memory/thought neurons for the next day. I then often have an urge to get up and continue with the problem. When I am working on non-math issues (e.g. planning the details of a project), I remember less of what I have dreamed and I could not detect a recurring pattern.
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Re: Math on the Brain?

Postby neuro on May 19th, 2016, 2:56 am 

I believe that most of this discussion is vitiated by the common misconception that a cerebral area is in charge of a function.

Higher functions can be performed thanks to the integration of the work of a number of cerebral areas, each of which has an internal circuital organization that makes it particularly apt to perform a certain kind of elaboration. Current cognitive neuroscience is based on the concept that each cerebral area is a "computational module" that performs especially well a specific kind of computation, which will enter in most high level functions of the brain.

For example, language requires a memory storage (for words), a semantic module, that can pick the right word, a premotor component, that can rehearse the sentence, a motor component that produces verbalization, a phonological loop that momentarily saves and can replay sounds so that we can go back and re-read what we hear to understand it, a visual memory for written word and a visual system capable of detecting the general shape of words and understanding them even if we only previece the frist and lsat chrcatear of the snetnece, and so on; one enormos burden of work in language is delegated to the cerebellum that, in a purely automatic, autopilot and unconscious way, performs all grammatical functions and checks (conjugating verbs, ordering the words in a sentence, etc). Each of these functions is performed in distinct areas.

As regards maths competence, a crucial role is played by spacial reasoning (mostly carried on by parietal regions). Geometrical competence is obviously based on the capability of visualizing in space. But also cardinality is based on (1) the innate capability of recognizing singularity, duality, and possibly up to 4-5 elements by the simultaneous analysis of several elements in a single picture (some animals can do it) and (2) the capability of mapping numbers as an ordered series (in space): think of 1, 2, 3 .... 1000... Isn't 1 just here and 1000 down there to the right?

Ordinality is based on size comparison (a visuo-spatial analysis).
A number of cognitive elaborations in maths are based on consequential logics (i.s. detecting / implying a causal relation between events / statements) and therefore use (prefrontal) circuits that are usually in charge of simulating, predicting and anticipating, and of strategical programming of behaviour. This, however, is called "central executive" module of "working memory", so it must obviously be involved in any kind of logical, rational, conscious elaboration.

We could go on like this for a while.
Language only comes about when we have to explicitly settle down what we have arrived at, to be able to recall it clearly, to communicate it to others, to symbolize it (e.g. in an equation) so that we can subsequently use the concept as something that has been solidly acquired.
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Re: Math on the Brain?

Postby Eclogite on May 19th, 2016, 6:28 am 

Dave_Oblad » Wed May 18, 2016 11:21 pm wrote:Here is an observation I'd like some feedback on. Most of the Dreams I have use no words. I can't even recall ever having a conversation in a dream. Most of my dreams involve situations I'm trying to resolve.. like finding my car in a parking lot. (I hate that dream as it's rather frequent.) How frequently do you dream using words in your dream?
That is very interesting and highlights a point made by someone earlier that there is likely much variety in how we think.

I definitely have extensive conversations in my dreams. This includes making detailed arguments for or against particular positions or actions, telling jokes, making puns, explaining things, commentary on what is occurring, etc. I am sure some dream segments are word-free, but for me dialogue, or monologue is the prevailing format.
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Re: Math on the Brain?

Postby jocular on May 19th, 2016, 8:55 am 

neuro » May 19th, 2016, 2:56 am wrote:I believe that most of this discussion is vitiated by the common misconception that a cerebral area is in charge of a function.

Higher functions can be performed thanks to the integration of the work of a number of cerebral areas, each of which has an internal circuital organization that makes it particularly apt to perform a certain kind of elaboration. Current cognitive neuroscience is based on the concept that each cerebral area is a "computational module" that performs especially well a specific kind of computation, which will enter in most high level functions of the brain.

For example, language requires a memory storage (for words), a semantic module, that can pick the right word, a premotor component, that can rehearse the sentence, a motor component that produces verbalization, a phonological loop that momentarily saves and can replay sounds so that we can go back and re-read what we hear to understand it, a visual memory for written word and a visual system capable of detecting the general shape of words and understanding them even if we only previece the frist and lsat chrcatear of the snetnece, and so on; one enormos burden of work in language is delegated to the cerebellum that, in a purely automatic, autopilot and unconscious way, performs all grammatical functions and checks (conjugating verbs, ordering the words in a sentence, etc). Each of these functions is performed in distinct areas.

As regards maths competence, a crucial role is played by spacial reasoning (mostly carried on by parietal regions). Geometrical competence is obviously based on the capability of visualizing in space. But also cardinality is based on (1) the innate capability of recognizing singularity, duality, and possibly up to 4-5 elements by the simultaneous analysis of several elements in a single picture (some animals can do it) and (2) the capability of mapping numbers as an ordered series (in space): think of 1, 2, 3 .... 1000... Isn't 1 just here and 1000 down there to the right?

Ordinality is based on size comparison (a visuo-spatial analysis).
A number of cognitive elaborations in maths are based on consequential logics (i.s. detecting / implying a causal relation between events / statements) and therefore use (prefrontal) circuits that are usually in charge of simulating, predicting and anticipating, and of strategical programming of behaviour. This, however, is called "central executive" module of "working memory", so it must obviously be involved in any kind of logical, rational, conscious elaboration.

We could go on like this for a while.
Language only comes about when we have to explicitly settle down what we have arrived at, to be able to recall it clearly, to communicate it to others, to symbolize it (e.g. in an equation) so that we can subsequently use the concept as something that has been solidly acquired.

That is interesting. Can we talk of a "software" that allows these different parts of the brain to "talk to the boss" as it were?

If we can , would it be some kind of a dynamic ,self regulating mechanism ,possibly without any identifiable physical "centre"?

I understand one of the reason brain implants (from one person to another) is impossible is that there is no method for the brain to communicate with the new "spare parts" .
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Re: Math on the Brain?

Postby TheVat on May 19th, 2016, 12:05 pm 

Here is an observation I'd like some feedback on. Most of the Dreams I have use no words. I can't even recall ever having a conversation in a dream. Most of my dreams involve situations I'm trying to resolve.. like finding my car in a parking lot. (I hate that dream as it's rather frequent.)
- DaveO

I have a similar experience with dreams. Like the parking lot dream, they often involve terrains or spaces or architectures that must be somehow navigated or "fixed" in some way. Maybe this is common in people with engineering/science/architecture brains. The dreams rarely have verbal content unless it's one of those semi-waking dreams where I have started to consciously be aware it's a dream and I try to exercise some control over the narrative and keep it going a little longer (especially if it's a pleasant one). Those, for some reason, may have a bit of verbal exchange, though the dialog often proves to be nonsensical if I completely wake up and tell my wife about it. It will seem to make sense in the dream, but then I wake up and it's stuff like "We have to go back and reverse the curl of the dog who put spokes in the cabinet."

I think the parking lot dream falls under the category of a dream about the natural fear of aging. Those of us with good spatial skills (probably many members of SPCF?) would feel anxious that these skills could erode and something we now find easy, like finding our car, might become hard for us. I am 60 and feel I'm at sort of a peak/plateau right now, so I can imagine hunting for my car at some future point and facing the realization that some cognitive skills don't last. I think it's likely that judgment, wisdom, the capacity to read people, and see the "big picture," may persist, but I have to recognize that I may forget where my keys or my car are located, or have trouble thinking of a certain word...and that's if I'm lucky and don't develop some form of dementia, like Alzheimer's.

Bit of a digression. That happens when you get older. :-D
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Re: Math on the Brain?

Postby neuro on May 19th, 2016, 12:58 pm 

jocular » May 19th, 2016, 1:55 pm wrote:That is interesting. Can we talk of a "software" that allows these different parts of the brain to "talk to the boss" as it were?

Pardon me, but who's supposed to be the "boss" here?
The elaboration activity itself essentially is the whole story.

If we can , would it be some kind of a dynamic ,self regulating mechanism ,possibly without any identifiable physical "centre"?

Correct, I'd say
I understand one of the reason brain implants (from one person to another) is impossible is that there is no method for the brain to communicate with the new "spare parts" .

I'm not so sure about that. In principle, you can read nervous activity, since it is electrical activity, and you can guide nervous activity by means of electrical impulses.

You can implant a multielectrode plate onto the motor cortex of a person who is paralized due to a spinal lesion and have her brain "talk" with a computer to move a robot, or even to stimulate the muscles of the person herself to produce movements...
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Re: Math on the Brain?

Postby jocular on May 19th, 2016, 1:41 pm 

neuro » May 19th, 2016, 12:58 pm wrote:
jocular » May 19th, 2016, 1:55 pm wrote:That is interesting. Can we talk of a "software" that allows these different parts of the brain to "talk to the boss" as it were?

Pardon me, but who's supposed to be the "boss" here?
The elaboration activity itself essentially is the whole story.

Is there not considered to be some kind of a mechanism that "draws all the threads together" -what I called "the boss" ?

If we can , would it be some kind of a dynamic ,self regulating mechanism ,possibly without any identifiable physical "centre"?

Correct, I'd say
I understand one of the reason brain implants (from one person to another) is impossible is that there is no method for the brain to communicate with the new "spare parts" .

I'm not so sure about that. In principle, you can read nervous activity, since it is electrical activity, and you can guide nervous activity by means of electrical impulses.

You can implant a multielectrode plate onto the motor cortex of a person who is paralized due to a spinal lesion and have her brain "talk" with a computer to move a robot, or even to stimulate the muscles of the person herself to produce movements...

I see what you mean. I was thinking about transplants from one brain to another.... Perhaps the level of sophistication of communication between artificial brain prostheses does not need to be anything near to that in a normal brain to be of value. Does the brain itself do all the "heavy lifting"?

Thanks for taking my post seriously (so far) . I have to admit to winging it and have very little knowledge of the subject -even though it is a very intimate one.


EDIT: apologies for the messy post. I am all at sea with mulltiquoting and arranging quotes within quotes.

So I used the red font to separate it out....
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Re: Math on the Brain?

Postby neuro on May 19th, 2016, 3:51 pm 

jocular » May 19th, 2016, 6:41 pm wrote:Is there not considered to be some kind of a mechanism that "draws all the threads together" -what I called "the boss" ?

I think this is the general (unsubstantiated) misconception.
There is no spectator for whom the brain plays its piece.
You should read Antonio Damasio's "Descartes' error".
Current opinion among scientists is that the neural activity itself, of a diffuse type, with several subsystems performing separate, partly independent tasks, and an intense intercommunication among them (through either direct cortico-cortical connections or cortico-thalamic and thalamo-cortical connections) gives rise to consciousness.

The alternative view - the so-called "dualistic" view - holds that something not strictly biological (spirit, soul) "reads" the activity of the brain (draws all the threads together). The problem with this view is even harder than the problem you raise for brain transplant: how would this entity communicate with the brain?
I see what you mean. I was thinking about transplants from one brain to another.... Perhaps the level of sophistication of communication between artificial brain prostheses does not need to be anything near to that in a normal brain to be of value. Does the brain itself do all the "heavy lifting"?

Not exactly, if I understand what you mean by "heavy lifting": you need a sophisticated learning software: it records the activity of the brain when the paralyzed subject, for example, tries to move a hand or to perform other movements; the procedure is repeated several times until the software becomes able to clearly distinguish the different activities of the brain, and then it will be able to have a robot perform the appropriate task next time the subject thinks of moving the arm or something else.
So I used the red font to separate it out....

You just need to insert a [/quote] string to interrupt a quote, then you insert your response and insert [quote] to continue the quote.
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Re: Math on the Brain?

Postby Dave_Oblad on May 20th, 2016, 6:34 pm 

Hi BiV,

Actually, I know the base fear in my dreams is about having something of mine stolen.

For example: (Dreams) I'm at a party and I hear someone say that the party is moving to another location. I know I left my car parked at the corner.. but when I get there it's gone...stolen. Same with the parking lot.. there is an empty space where I know I parked my car. Or.. I work someplace and the company is moving to another building, so all my stuff is getting boxed up. When I get to the new building, someone(s) have/had raided my box of equipment and all my test gear has been distributed to many other employees work stations and they claim that my stuff has always been theirs.

So, it's not really about misplacing something but rather having lost something because it was stolen. I strongly suspect the source of his fear is related to an incident that happened. I had my hobby shop with $1000,s of dollars worth of electronics equipment in my spare bedroom. We took in a guest/roommate.. so I moved all my stuff into a storage locker at my apartment building and locked it. Some old lady downstairs told the Manager that someone had put a lock on her locker and insisted the manager cut off the lock to access her belongings. She was mistaken, her assigned locker was next to mine.. mine now minus a lock. The manager had partially emptied my locker to the floor before the old lady decided to try her key on her actual locker and it opened. By now a crowd had grown watching the show, according to a witness.

The manager put my stuff back in my locker and close my locker (minus a lock). He left me a note on my Apt door to tell me I had to replace my lock on my locker. When I got home, read the note and looked inside my locker.. all my valuable stuff was gone.. stolen. I was super angry with the manager.. but he was literally mentally challenged.. could barely read. Short version ending: That was the end of my 10+ years hobby in Electronics. That's basically how I learned electronics.. via hobby. After that incident I bought an Atari Computer and started a new hobby in writing software and making games.

Anyway, that anger and frustration is what I believe is reflected in my (not so fun) Dreams since.

Ok.. sorry to drag off topic.

Regards all,
Dave :^)
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Re: Math on the Brain?

Postby dandelion on May 22nd, 2016, 10:44 am 

The dream discussion was really interesting. Some of it was fascinating because those rather recurring driving/walking (/river paddling) dreams are really familiar to me, set in about four fairly distinct settings since childhood (the driving across town dream I’ve had since long before I learnt to drive), involving things like navigating with mental maps, recalling features and directions with seemingly exaggerated complexity. I think they could happen mostly when I’ve been thinking about visual and spatial things, but to do with aesthetic designs and judgements. Although those dreams aren’t verbal usually, that is unusual for my dreams because generally there isn’t much chat, but some at least. I consider myself a far more a visual than verbal person, while my husband, who talks and uses maths much more than I do, says he doesn’t recall any dialogue in dreams.

Regarding the paper and neuro’s comments, I’m not sure what was meant by misconceptions with areas in charge of functions, so am likely culpable. I could also be mixed up with definitions of (natural or syntactic and semantic) language, maths, or symbols, or various types of memory, and innateness too. For example, a quick google search likened symbols in a similar context with digits or discreteness, and in this thread symbolism was linked with consolidation, allowing further use in communication. The innate capability for recognising singularity and some other small quantities by simultaneous analysis, and holding the result for some time to be useful, seems rather like innate symbols in this context? I’m not sure whether the comments meant language is necessary for all (non-innate) symbolisation, for a type of symbolisation for all communication, or for a type of communication? For reasons like this, I’m not sure how the comments fit with things written in the paper, like mention that language in earlier learning isn’t necessarily ruled out, the term, “reflection”, and whether working memory employs symbols, made with or without language, and if such sorts of things are communicable.

‘Except for a small additional activation in posterior inferotemporal and posterior parietal cortex for geometry statements, all problems in algebra, analysis, topology, and geometry induced correlated and overlapping activations that systematically spared language areas. Using elementary algebraic and arithmetic stimuli, previous fMRI and neuropsychological research in nonmathematicians also revealed a dissociation between mathematical and syntactic knowledge (19, 22, 26, 45). Together, those results are inconsistent with the hypothesis that language syntax plays a specific role in the algebraic abilities of expert adults. Importantly, however, they do not exclude a transient role for these areas in the acquisition of mathematical concepts in children (10). Imaging studies of the learning process would be needed to resolve this point.

‘Our results should not be taken to imply that the IPS, IT, and PFC areas that activated during mathematical reflection are specific to mathematics. In fact, they coincide with regions previously associated with a “multiple-demand” system (29) active in many effortful problem-solving tasks (30) and dissociable from language related areas (46). Some have suggested that these regions form a “general problem solving” or “general purpose network” active in all effortful cognitive tasks (47). Several arguments, however, question the idea that this network is fully domain-general. First, we found no activation of this network during equally difficult reasoning with nonmathematical semantic knowledge. In fact, the easiest mathematical problems caused more activation than the most difficult nonmathematical problems (Fig. 5), and even meaningless mathematical problems caused more activation than meaningful general-knowledge problems (Fig. 4). Second, other studies have found a dissociation between tightly matched Amalric and Dehaene PNAS Early Edition | 7 of 9 PSYCHOLOGICAL AND COGNITIVE SCIENCES NEUROSCIENCE INAUGURAL ARTICLE conditions of linguistic versus logical or arithmetical problem solving (19, 48). Overall the existing literature suggests that the network we identified engages in a variety of flexible, abstract, and novel reasoning processes that lie at the core of mathematical thinking, while contributing little to other forms of reasoning or problem solving based on stored linguistic or semantic knowledge.’
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Re: Math on the Brain?

Postby nerd01 on May 23rd, 2016, 8:03 am 

High-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit as suggested by the evidence.
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Re: Math on the Brain?

Postby dandelion on May 29th, 2016, 5:27 am 

On things like navigation during sleep, this is long but discusses things rat sleep navigation replays. It is about grid cells and other cells like place cells, including a cell that fires for particular objects, food source, etc., and trace cells and involvement of memory of particular objects. https://www.youtube.com/watch?v=BEScyWMvSKk

It also mentions memory of scent with rats and impact of environment in young rats on formation of grid cells. The recent experiment with scents in the video is a bit like one published by OUP in 2005, by Galef, but in this earlier experiment information seems acquired from a brief interaction with a fellow demonstrator rat. Galef also showed a strong social impact on rat consumption of food not previously eaten, involving odours and scent trails. Also re rats and scents, a study from 2001 by Campbell and Heyes where instead of showing rats imitating from a visual demonstration a rat’s successful lever direction choice, up or down, rat direction choice seems to have been modified by demonstrator rat odour deposits, above or below.

I’d written a confusing post and would be interested in more ideas. Also, Dave O's equipment loss sounds terrible.
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