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)?
When Blind People Do Algebra, the Brain's Visual Areas Light Up
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Re: When Blind People Do Algebra, the Brain's Visual Areas Light Up
#62Does 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)?
That's an interesting question. I don't know an answer, but I did find this post about an old experiment: https://mindhacks.com/2009/11/18/do-blind-people-hallucinate...
It's very unlikely that anything similar would be done today.
Re: When Blind People Do Algebra, the Brain's Visual Areas Light Up
#63This 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.
Re: When Blind People Do Algebra, the Brain's Visual Areas Light Up
#64If 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 w…
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.
Re: When Blind People Do Algebra, the Brain's Visual Areas Light Up
#65As 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.
[1] http://m.pnas.org/content/113/18/4909.abstract?sid=fae659df-...
Re: When Blind People Do Algebra, the Brain's Visual Areas Light Up
#66Are we ever going to move past this 'what parts light up' stage of neuroscience? one-trick-pony science.
The research community is way past that stage already.
This is a journalistic account of a scientific result. It's important to keep that in mind.
Re: When Blind People Do Algebra, the Brain's Visual Areas Light Up
#67Would it be fair and/or relevant to say that all areas of math can be represented geometrically
I dunno. 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…
https://www.quantamagazine.org/20130917-a-jewel-at-the-heart...
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 ?