We show how an epistemology informed by cognitive science promises to shed light on an ancient problem in the philosophy of mathematics: the problem of exactness. The problem of exactness arises because geometrical knowledge is thought to concern perfect geometrical forms, whereas the embodiment of such forms in the natural world may be imperfect. There thus arises an apparent mismatch between mathematical concepts and physical reality. We propose that the problem can be solved by emphasizing the ways in which the (...) brain can transform and organize its perceptual intake. It is not necessary for a geometrical form to be perfectly instantiated in order for perception of such a form to be the basis of a geometrical concept. (shrink)

The coding mechanism of sensory memory on the neuron scale is one of the most important questions in neuroscience. We have put forward a quantitative neural network model, which is self-organized, self-similar, and self-adaptive, just like an ecosystem following Darwin's theory. According to this model, neural coding is a “mult-to-one”mapping from objects to neurons. And the whole cerebrum is a real-time statistical Turing Machine, with powerful representing and learning ability. This model can reconcile some important disputations, such as: temporal coding (...) versus rate-based coding, grandmother cell versus population coding, and decay theory versus interference theory. And it has also provided explanations for some key questions such as memory consolidation, episodic memory, consciousness, and sentiment. Philosophical significance is indicated at last. (shrink)

We explore the nature of forgetting in a corpus of 125,000 students learning Spanish using the Rosetta Stone® foreign-language instruction software across 48 lessons. Students are tested on a lesson after its initial study and are then retested after a variable time lag. We observe forgetting consistent with power function decay at a rate that varies across lessons but not across students. We find that lessons which are better learned initially are forgotten more slowly, a correlation which likely reflects a (...) latent cause such as the quality or difficulty of the lesson. We obtain improved predictive accuracy of the forgetting model by augmenting it with features that encode characteristics of a student's initial study of the lesson and the activities the student engaged in between the initial and delayed tests. The augmented model can predict 23.9% of the variance in an individual's score on the delayed test. We analyze which features best explain individual performance. (shrink)