A functional MRI study of 17 people blind since birth found that areas of visual cortex became active when the participants were asked to solve algebra problems, a team from Johns Hopkins reports in the Proceedings of the National Academy of Sciences.
Yeah, I'm gonna take this study with a grain of salt. Too many "fMRI studies of 17 people" have turned out to be barely disguised hooey.
Just because the bug was discovered doesn't mean it's been fixed in deployment. ;)
Remember, as well, the bug was only half of that paper's findings; they also found fundamental flaws in the method. Besides which, there are widespread methodological flaws that IMO make more difference.
I heard the visual areas were predetermine simply because the oculor nerved terminates there. So if somebody was blind from birth they're claiming that some specialization might be hardcoded after all.
This seems to provide once more evidence for the hypotheses that the cortex implements some sort of general purpose algorithm. The visual cortex of a blind person does not receive any sensory information, but just information from other cortical areas. Perhaps it then simply learns (by reward modulation) to augment the high-order association that occurs in the occipital lobe. Interesting stuff.
>the cortex implements some kind of general purpose algorithm
That algorithm is really just the laws of physics being followed in a very, very complex system.
Not to be overly pedantic, but when you say "some sort of general algorithm," what do you mean? Do you mean that there is some sort of information processing in the cortex (everyone's cortex!) that could be written down and named "the process of cognition"?
Perhaps by "some sort of general algorithm" you really mean the mechanisms underlying neuroplasticity, which are what enable learning and memory and this arguably the ability to have what we call consciousness?
I don't mean to nitpick (and I don't think I am) but this tendency among HN comments to try to shoehorn principles of computing into an alleged understanding of cognition seems to be both popular and, well, unsupported by any existing science.
I get your point but it's absurd to call V1 - V3 an "algebra area". We actually do have a thing called "primary visual cortex" and mental calculations are known to exploit a number of existing functional areas (visual word-form area, primary visual cortex, etc).
The point is that it's pretty clearly a visual area above all else. The pathway from the eye to V1 is possibly the most extensively studied functional neuroanatomical pathway in the brain.
It's also well-established that it takes input from other regions and that this adjusts visual percepts. The idea that mathematical operations recruit visual areas is unsurprising and predicted by every theory of numerical cognition there is. That's why this is interesting.
I'm sorry, but what you're claiming is patently absurd (and, I suspect, purely contrarian).
This is perhaps a poor backup claim because I can't give a relevant citation, but back when I was in Neuroscience / neuroanatomy in medical school, I remember feeling deeply impressed at the level to which we do understand the visual processing system in the brain. Its far more comprehensive than simple imaging studies -- we know where the wires go, how the photons are transduced and turned into patterns of neurons firing, etc. There's of course plenty to learn but our depth of understanding in regards to human vision is impressive.
I'm pretty sure that I engage the visual part of my brain in those moments when I truly understand algebra. It's very beautifully overwhelming and understanding such complex mathematics through visualisation brings about one of the few moments where I get naturally high through cognitive tasks.
I wouldn't consider myself a very visual person otherwise.
> I'm pretty sure that I engage the visual part of my brain in those moments when I truly understand algebra.
With no offence meant to your self knowledge, and with the understanding that you were probably not one of those tested and that our (meaning their, I guess) understanding of the workings of the brain is imperfect, I think that the point of brain imaging software is in large part so that we don't have to rely on "I'm pretty sure", and indeed can have confidence even in unintuitive conclusions.
> With no offence meant to your self knowledge, and with the understanding that you were probably not one of those tested and that our (meaning their, I guess) understanding of the workings of the brain is imperfect, I think that the point of brain imaging software is in large part so that we don't have to rely on "I'm pretty sure", and indeed can have confidence even in unintuitive conclusions.
Self-knowledge is not a good way to divine the functioning of the brain. However, one could say fMRI is not a good way either, at the very least studies based solely on fMRI data should be taken with a boatload of salt. See for example:
http://www.pnas.org/content/113/28/7900.full
> Functional MRI (fMRI) is 25 years old, yet surprisingly its most common statistical methods have not been validated using real data. Here, we used resting-state fMRI data from 499 healthy controls to conduct 3 million task group analyses. Using this null data with different experimental designs, we estimate the incidence of significant results. In theory, we should find 5% false positives (for a significance threshold of 5%), but instead we found that the most common software packages for fMRI analysis (SPM, FSL, AFNI) can result in false-positive rates of up to 70%. These results question the validity of a number of fMRI studies and may have a large impact on the interpretation of weakly significant neuroimaging results.
It's possible. That would still fit the general premise that people can "rewire" their own brains through use. One of the leading theories of Synesthesia is that different areas of the brain are not separated: https://en.wikipedia.org/wiki/Neural_basis_of_synesthesia#Cr...
It would follow that it is possible that they could then be rejoined as well.
I'm the same way and came to a similar conclusion a while back. For me, understanding math has been an incredibly visual process more than anything. It's a very useful heuristic. Programming is similar, but its discreteness seems to make it significantly less visual.
This comment reminds me of high school physics, when we were learning about interference and those double slit experiments. The teacher would give different scenarios and ask us to predict what patterns would be observed. In one, the pattern was alternating bands of dark and light. I was the only kid who could figure it out, and the physics teacher was so visibly impressed, he to started calling me the thinker. That thing, visualizing something given to you in mathematical form, feels very good indeed.
> That thing, visualizing something given to you in mathematical form, feels very good indeed
I agree completely. I still remember the feeling I got when I was able to visualize differential equations in relation to "normal" calculus. It completely changed the way I thought about math.
Joo Janta 200 Super-Chromatic Calculus Sensitive Sunglasses have been specially designed to help people develop a relaxed attitude to calculus. At the first hint of calculus, they turn totally black and thus prevent you from seeing anything that might alarm you.
If areas of the brain could have any purpose, why are the same purposes allocated to the same areas in each person? This doesn't make any sense to me. Of course, brains aren't totally uniform, but the fact that you can say "x area is used for y activity in general" seems pretty absurd.
Or maybe there is a particular, most efficient arrangement of departments. But surely this can't be achieved in every individual. I wish studies didn't try to be as general sometimes - the anomalies are more interesting.
For one sensory input nerves and motor output nerves have distinct entry/exit points. I.e. visual preprocessing must ofcourse take place in the brain where the optical nerves enter.
This is an excellent question, and an unanswered one. I want to add that functional areas of the brain are not 100% consistent and in fact vary not only by handedness but also by enough that a neurosurgeon cannot confidently operate on a specific location of the brain without first verifying what functionality it exhibits.
That said, the remarkable consistency of the location of, say, Broca's area, has always baffled me. Human DNA encodes signals that trigger the development of the neural tube and later the nervous system; that much is understandable - but how could it be possibly also encoding enough information to consistently result in similar functionality in similar areas?
As someone that has done an undergraduate fellowship in mathematical modeling of plasticity in large neural networks (and thus knows just enough to be confident about being wrong without realizing it), my personal mental model for this is that a functional area arises in an essentially deterministic manner based on its inputs - the auditory nerves, optic nerves, sensory input, and so on; the initial neural network must have no predetermined function and instead must have its functionality arise as a consequence of recurrent associations between input, output, and subsequent input, and so on.
That is, if a certain area receives visual input, it will adapt to discriminate details in visual sensory information, and similarly with auditory input, and so on - and eventually the only place that, say, Broca's area for language _could_arise is at the intersection of a particular set of sensory inputs.
As I said, this is essentially layman speculation. Furthermore, I try to imagine the computational complexity of demonstrating such determinism using a model, and it is staggering. There are on the order of 10^11 neurons, each of which is not only a very complex biochemical unit on its own but also can be modulated by or modulate up to something like 100,000 other neurons - let alone simulating the input to such a model.
It truly is staggering. We know so little, and it isn't even clear where to look to find out what we don't know we don't know.
There's a lot of conceptual metaphors and sometimes even structure from geometry in higher maths, but this is sometimes very abstract and merely makes reference to non-geometric ideas about geometry previously developed.
For example, in the kind of stochastic calculus quant finance people learn, there's an isometry (like a transformation that preserves size in some sense) between two very different kinds of continuous, non-enumerable spaces. Geometric intuition is of no help there -- you did learn what an isometry was in high school so you know the word, but you can't see function spaces in any way, shape or fashion.
OTOH what I'm working on for my dissertation is "geometric integrators" for certain kinds of differential equations where the isometries and references to geometry are more direct; basically, the most common numerical solvers for initial value problems in ODEs preserve certain invariants and are useful for many many problems, but sometimes you want computation to preserve some sense of volume -- clasically, in mechanics. So even though many problems are too abstract to be seen, the notion of volume conservation is the best way to acquire the basic notions of the field.
To even hint that the above breakthrough could possibly be relevant to this thread's subject would qualify as a form of quantum mysticism, wouldn't it ?
Yes, as a mathematical object, that is true. But any symbol we render in the physical world is going to be finite.
Drawing a straight mark and calling it an infinite set of points isn't really different from drawing a sideways 8 and calling it an infinite set. It's a symbol that represents something else.
There is nothing special about algebra in that regard. Ask blind person to recall some visual memory (from before they went blind, obviously) and the effect is exactly the same. Or ask any healthy person to close one's eyes and do algebra - still the same effect.
The point is: our brain does not really tells apart reality from imagination. The same areas are involved in processing real images comming from the eyes, as well as internally "rendered" imaginary images.
The study examined people blind since birth. But the article doesn't say much about the degree of their visual impairment—there's a big difference even between "no light perception" and "light perception only" (where people can still get visual information useful for orientation), much less higher amounts of vision.
If the study was restricted to people with no light perception since birth, that's a very small population, getting a larger sample might be difficult.
Maybe what they considered visual includes abstract spatial (mentioned) areas, and abstract distances (n-dimensional differences) are the bread and butter of reflection.
It's a good question, I've been asking that myself.
I have recently befriended a post-doc in neuroscience and in one of his lectures he referred to "part of brain lighting up" as a legitimate research method. So it's not pop-science, it's how the actuals science is being done today.
The brain is vast in it's complexity, so much so that we don't even grasp the magnitude of the complexity itself. There are between 10^11 and 10^13 neurons, depending on the method of approximation. There are 10^4 dendrites (inputs) to each neuron, and one output (axon). The inputs are analogue and mediated by chemistry. The output is binary, thankfully, however the axon is fairly long and itself can go in/out of order based on certain chemical balance along its entire length.
There is an old idea that the visual cortex involved when we visualize past experiences or memorized material. It probably has a recall machinery.
With the blind subjects, perhaps, this activity (dealing with abstractions) has been registered as a distinct (due to lack of sensory input), while in the control group it is drowned in the noise of normally functioning visual cortex.
So, it is interesting but inconclusive. Also fMRI can't be used as a method of discovery, because it is based on very approximate statistical models. Something is going on there. Well, there always something is going on.
You could instead speculate that what we consider the "Visual Areas" of the brain are more than that. Hence we have been wrong about those parts of the brain.
Does this mean that, if blind people take some drug that has an effect on the "visual areas", their math gets screwed up? What if you gave them a - for sighted people - highly visual psychedelic, will their algebra be all weird (or, weird in a different way than it would be for a sighted person)?
As someone with a graduate degree in mathematics, I not only find the result with blind people unsurprising but also doubt the veracity of the results with sighted people. Let me elaborate.
Pure mathematics, at a high level, seeks for formalize some sort of observable, intuitive behavior in an experientially accessible system and then generalize it to an abstract degree that is no longer anything to do with experience. For example, counting pebbles directly leads to the positive integers, but you can construct the real numbers, almost all of which are uncomputable and/or transcendental, starting entirely from the integers. When doing high school algebra, we are reasoning about quantities and moving them around, so it makes sense that an otherwise underutilized visual cortex would be used for this purpose in a blind person, especially considering that he would need to construct a more elaborate mental model as a consequence of being unable to look at scratch paper.
I would not expect a random sample of sighted people to show activation of visual or spatial reasoning areas just because math education is so poor and so many people get through it by memorization rather than employing abstract reasoning skills based on spatial reasoning - in fact, I would expect increased activation of areas related to language. I would expect fMRI imaging of mathematicians, in contrast, to show high activations of areas to do with spatial reasoning, and perhaps even visual processing. See, for example, [1], which provides evidence for this hypothesis.
Drawing on personal experience, I learned the basic concepts of linear algebra by direct analogy to three-dimensional visualization, which is of course experientially already present. However, as I progressed and studied n-dimensional vector spaces, I no longer had an experiential analog - and yet I still use some of the same spatial reasoning abstractions (in a different, extended and/or generalized way) when reasoning in the N-dimensional case.
My opinion is that this study should have included an experimental group of trained mathematicians (or at least advanced mathematics students with demonstrated mathematical reasoning skills), and I again point to [1] for some degree of justification for this stance.
66 comments
[ 10.7 ms ] story [ 274 ms ] threadYeah, I'm gonna take this study with a grain of salt. Too many "fMRI studies of 17 people" have turned out to be barely disguised hooey.
Remember, as well, the bug was only half of that paper's findings; they also found fundamental flaws in the method. Besides which, there are widespread methodological flaws that IMO make more difference.
That algorithm is really just the laws of physics being followed in a very, very complex system.
Not to be overly pedantic, but when you say "some sort of general algorithm," what do you mean? Do you mean that there is some sort of information processing in the cortex (everyone's cortex!) that could be written down and named "the process of cognition"?
Perhaps by "some sort of general algorithm" you really mean the mechanisms underlying neuroplasticity, which are what enable learning and memory and this arguably the ability to have what we call consciousness?
I don't mean to nitpick (and I don't think I am) but this tendency among HN comments to try to shoehorn principles of computing into an alleged understanding of cognition seems to be both popular and, well, unsupported by any existing science.
https://en.wikipedia.org/wiki/Inattentional_blindness
I mean it's not like there's an owners manual for the human brain.
It's also well-established that it takes input from other regions and that this adjusts visual percepts. The idea that mathematical operations recruit visual areas is unsurprising and predicted by every theory of numerical cognition there is. That's why this is interesting.
I'm sorry, but what you're claiming is patently absurd (and, I suspect, purely contrarian).
I tend to agree with the premise of the article, which is brain areas can be reapportioned for different tasks.
I wouldn't consider myself a very visual person otherwise.
With no offence meant to your self knowledge, and with the understanding that you were probably not one of those tested and that our (meaning their, I guess) understanding of the workings of the brain is imperfect, I think that the point of brain imaging software is in large part so that we don't have to rely on "I'm pretty sure", and indeed can have confidence even in unintuitive conclusions.
Self-knowledge is not a good way to divine the functioning of the brain. However, one could say fMRI is not a good way either, at the very least studies based solely on fMRI data should be taken with a boatload of salt. See for example: http://www.pnas.org/content/113/28/7900.full
> Functional MRI (fMRI) is 25 years old, yet surprisingly its most common statistical methods have not been validated using real data. Here, we used resting-state fMRI data from 499 healthy controls to conduct 3 million task group analyses. Using this null data with different experimental designs, we estimate the incidence of significant results. In theory, we should find 5% false positives (for a significance threshold of 5%), but instead we found that the most common software packages for fMRI analysis (SPM, FSL, AFNI) can result in false-positive rates of up to 70%. These results question the validity of a number of fMRI studies and may have a large impact on the interpretation of weakly significant neuroimaging results.
It would follow that it is possible that they could then be rejoined as well.
http://worrydream.com/LearnableProgramming/
I agree completely. I still remember the feeling I got when I was able to visualize differential equations in relation to "normal" calculus. It completely changed the way I thought about math.
That said, the remarkable consistency of the location of, say, Broca's area, has always baffled me. Human DNA encodes signals that trigger the development of the neural tube and later the nervous system; that much is understandable - but how could it be possibly also encoding enough information to consistently result in similar functionality in similar areas?
As someone that has done an undergraduate fellowship in mathematical modeling of plasticity in large neural networks (and thus knows just enough to be confident about being wrong without realizing it), my personal mental model for this is that a functional area arises in an essentially deterministic manner based on its inputs - the auditory nerves, optic nerves, sensory input, and so on; the initial neural network must have no predetermined function and instead must have its functionality arise as a consequence of recurrent associations between input, output, and subsequent input, and so on.
That is, if a certain area receives visual input, it will adapt to discriminate details in visual sensory information, and similarly with auditory input, and so on - and eventually the only place that, say, Broca's area for language _could_arise is at the intersection of a particular set of sensory inputs.
As I said, this is essentially layman speculation. Furthermore, I try to imagine the computational complexity of demonstrating such determinism using a model, and it is staggering. There are on the order of 10^11 neurons, each of which is not only a very complex biochemical unit on its own but also can be modulated by or modulate up to something like 100,000 other neurons - let alone simulating the input to such a model.
It truly is staggering. We know so little, and it isn't even clear where to look to find out what we don't know we don't know.
There's a lot of conceptual metaphors and sometimes even structure from geometry in higher maths, but this is sometimes very abstract and merely makes reference to non-geometric ideas about geometry previously developed.
For example, in the kind of stochastic calculus quant finance people learn, there's an isometry (like a transformation that preserves size in some sense) between two very different kinds of continuous, non-enumerable spaces. Geometric intuition is of no help there -- you did learn what an isometry was in high school so you know the word, but you can't see function spaces in any way, shape or fashion.
OTOH what I'm working on for my dissertation is "geometric integrators" for certain kinds of differential equations where the isometries and references to geometry are more direct; basically, the most common numerical solvers for initial value problems in ODEs preserve certain invariants and are useful for many many problems, but sometimes you want computation to preserve some sense of volume -- clasically, in mechanics. So even though many problems are too abstract to be seen, the notion of volume conservation is the best way to acquire the basic notions of the field.
To even hint that the above breakthrough could possibly be relevant to this thread's subject would qualify as a form of quantum mysticism, wouldn't it ?
Drawing a straight mark and calling it an infinite set of points isn't really different from drawing a sideways 8 and calling it an infinite set. It's a symbol that represents something else.
I thought it was cool when I first saw it. Infinity in the complex plane is one of the poles.
http://www.evanmiller.org/dont-kill-math.html
The point is: our brain does not really tells apart reality from imagination. The same areas are involved in processing real images comming from the eyes, as well as internally "rendered" imaginary images.
If the study was restricted to people with no light perception since birth, that's a very small population, getting a larger sample might be difficult.
I have recently befriended a post-doc in neuroscience and in one of his lectures he referred to "part of brain lighting up" as a legitimate research method. So it's not pop-science, it's how the actuals science is being done today.
The brain is vast in it's complexity, so much so that we don't even grasp the magnitude of the complexity itself. There are between 10^11 and 10^13 neurons, depending on the method of approximation. There are 10^4 dendrites (inputs) to each neuron, and one output (axon). The inputs are analogue and mediated by chemistry. The output is binary, thankfully, however the axon is fairly long and itself can go in/out of order based on certain chemical balance along its entire length.
It's a heck of a job.
This is a journalistic account of a scientific result. It's important to keep that in mind.
With the blind subjects, perhaps, this activity (dealing with abstractions) has been registered as a distinct (due to lack of sensory input), while in the control group it is drowned in the noise of normally functioning visual cortex.
So, it is interesting but inconclusive. Also fMRI can't be used as a method of discovery, because it is based on very approximate statistical models. Something is going on there. Well, there always something is going on.
You could instead speculate that what we consider the "Visual Areas" of the brain are more than that. Hence we have been wrong about those parts of the brain.
It's very unlikely that anything similar would be done today.
Pure mathematics, at a high level, seeks for formalize some sort of observable, intuitive behavior in an experientially accessible system and then generalize it to an abstract degree that is no longer anything to do with experience. For example, counting pebbles directly leads to the positive integers, but you can construct the real numbers, almost all of which are uncomputable and/or transcendental, starting entirely from the integers. When doing high school algebra, we are reasoning about quantities and moving them around, so it makes sense that an otherwise underutilized visual cortex would be used for this purpose in a blind person, especially considering that he would need to construct a more elaborate mental model as a consequence of being unable to look at scratch paper.
I would not expect a random sample of sighted people to show activation of visual or spatial reasoning areas just because math education is so poor and so many people get through it by memorization rather than employing abstract reasoning skills based on spatial reasoning - in fact, I would expect increased activation of areas related to language. I would expect fMRI imaging of mathematicians, in contrast, to show high activations of areas to do with spatial reasoning, and perhaps even visual processing. See, for example, [1], which provides evidence for this hypothesis.
Drawing on personal experience, I learned the basic concepts of linear algebra by direct analogy to three-dimensional visualization, which is of course experientially already present. However, as I progressed and studied n-dimensional vector spaces, I no longer had an experiential analog - and yet I still use some of the same spatial reasoning abstractions (in a different, extended and/or generalized way) when reasoning in the N-dimensional case.
My opinion is that this study should have included an experimental group of trained mathematicians (or at least advanced mathematics students with demonstrated mathematical reasoning skills), and I again point to [1] for some degree of justification for this stance.
[1] http://m.pnas.org/content/113/18/4909.abstract?sid=fae659df-...