The learning
Let me discuss Strang, Montessori, neuroscience and deep learning.
In lecture 1, professor Strang teaches the problem, shows the three perspectives to consider, poses the questions and concludes with the Ax = b description.
The problem is to solve n equations with n unknowns. It is that. There are the row picture, the column picture and the matrix form. Professor Strang demonstrates the limitation of the row picture method, where each row is considered first to solve a particular problem. He then shows how the column picture can tackle the problem better, even considering more dimensions. He states the importance of the column picture and describes that it is a linear combination. Proceeding to the matrix form, we then have Ax = b. A is a matrix, containing the numbers for a particular problem. The vector x contains the unknowns that we want to check exist to solve b.
Two questions are considered. Can I solve Ax equals b for every b? Does there exist a linear combination that solves for every b? You know, perhaps the second question is not exactly phrased like that, but that is the idea.
So, Ax = b. Professor Strang concludes showing how to multiply a matrix by a vector. Two methods. First, he shows a linear combination of the column vectors in A with each item in x as an accompanying term. And the second method as the dot product between each row vector in the matrix and the column vector x.
He concludes by describing that Ax is a linear combination of the columns of A. Really great.
Regarding Montessori, reading The Advanced Montessori Method. In Portuguese, it was translated as Autoeducação no Ensino Fundamental. I am reading this Portuguese text.
So, reading about exercises in which the children read phrases and interpret them with acting, thereby demonstrating that they understood. I then thought about the learning aspect. The children follow the program and the structure, the innate structure for learning is already there, available. It is not the training per se. Children in traditional schools learn, perhaps not in the most efficient way, perhaps not reaching their potential. This is obviously important, but does not prevent the learning process per se. So, the mystery lies in the mechanism of learning.
A work was published showing images of a small section of the brain showing in detail a neural network structure. It has so many neurons and the connections are complex. How can deep learning achieve the learning with a simpler structure? Scaling, perhaps, is not enough. But the current algorithms, are they the correct? It seems to me that it is deep learning, but progress needs to be considered in the foundations. The definition of the neuron and the interaction between the neurons. It is a really interesting challenge.
Why is that important? It is to serve humankind. The abundance that AI can provide could solve poverty on Earth. Superintelligence, beyond that, can lead humanity to not be distracted and wrong in earthly things, the materialist world, and can lead a person to Set Your Mind On Things Above. Special.