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9

Very many references may easily be found with a Google search for "mathematical model memory". Probably the most classic and iconic reference is Atkinson and Shiffrin (1965), which is also described on Wikipedia. Its three components and their relationships are nicely encapsulated in this figure: Many other, lesser-known mathematical models of memory ...


8

I would go with Physics. Physicists study the world using mathematics, while mathematicians study mathematics itself which is a construct that does not necessarily exist in the real world (Albert Einstein once said: "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."). ...


7

In general, there are two types of 'complexity' that are studied. Usually, when people talk about 'complexity', especially on the internet, they mean Santa Fe Institute style complexity. This is a vague and poorly defined concept that has struggled for a number of years without making significant progress. It uses pretty words, but has yet to deliver on any ...


6

I will deviate from the other answers and give more pessimistic response based on my experience as a mathematician and theoretical computer scientist that spends some of his time in a psychology department. In cognitive science, neuroscience, and psychology (like in most sciences) you will never do mathematics in the definition, lemma, theorem, proof ...


6

the question which of these two descriptions is correct? is perhaps natural in the context of, say, someone studying for an examination. epistemologists might suggest that a better formulation would be is either of these correct? however, as stated here there are clear reasons for preferring the first formulation to the second. I shall first explain why, ...


5

Thoughts on the paper The paper appears to provide a high level overview of the role of mathematics in cognitive science. I'm not a sufficient expert in the overall field of cognitive science where I'd feel comfortable to truly judge the accuracy of the overall synthesis that Andler (2012) provides. That said, much of the paper is about providing examples ...


5

Now that @ofri has presented a good argument for physics, I'll give a few arguments for the benefits of a course in maths, and particularly a math course that focuses heavily on statistics. There are many areas of psychology where a good understanding of statistics is very helpful. Statistics is particularly useful in psychometrics, mathematical ...


4

Thanks for sharing the article. I read the paper and what I take from it is a rather pessimistic view. He suggests that there is a crucial need for overarching proper mathematical modeling, but he makes it sound this is also a huge obsticle and we must wait (longer than a young persons academic career) to see the fruits of it. I'm coming from a theoretical ...


3

It's a little unclear what you're asking. In general, psychologists try to build models that are parsimonious; this often means only introducing new parameters (particularly free parameters) into a model when they are absolutely necessary. You are right that with a sufficient number of free parameters, one can build a model that fits the data perfectly. But ...


3

I would say that the maths that are most useful in cognitive science are the ones that have to do with decision theory. So I would include linear algebra (with its matrixes, and "transition" or changes of state analysis), as well as probability and statistics, with their "expected values" and resulting decision trees. Computational and information analysis, ...


3

It seems like there is a fairly big literature on this topic. Wagenaar (1972) provides an early review of research. The author summarises around 15 studies. The studies involved generated random elements including letters and numbers of varying lengths. In all but one study, participants were deemed to be not good at randomising. As part of their review ...


3

Semantic foraging in memory is another nice example: concepts in memory can be represented spatially as locations in multidimensional space, and the route we travel in that 'space' has a lot in common with the optimal foraging movements animals adopt. http://www.indiana.edu/~clcl/Papers/HTJ_Foraging.pdf


3

Here are a few off the top of my head from neuroscience: neural activity may primarily exist on low dimensional attractors. reconstructing PET signal origins from emitted gamma rays It's widely believed our brains are gyrencephalic (wrinkly) to maximize surface area. Various distance metrics (Euclidean, Mahalanobis) are common tools for clustering data, ...


1

Though not a direct bridge between Linguistics and Cognitive Science, Semasiographic communication systems are a ripe territory for the studio of Mereology. Off-hand, consider: Dewalque, A. Brentano and the parts of the mental: a mereological approach to phenomenal intentionality. Phenomenology and the Cognitive Sciences, September 2013, Volume 12, Issue ...



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