When Blind People Do Algebra, the Brain's Visual Areas Light Up
npr.org
npr.org
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.
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.
It would follow that it is possible that they could then be rejoined as well.
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).
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.
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.
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.
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-...
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.
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.
It's very unlikely that anything similar would be done today.
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.
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 ?
I thought it was cool when I first saw it. Infinity in the complex plane is one of the poles.
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.