Machines and Reasoning
An abstract machine is a result of capturing the essence of reasoning by a set of small procedures called algorithm. Machines were created to solve problems and the Digital Electronic Machines (DEM) are useful for the intellectual pursuit of anyone capable of operating it. The digital computer is an extension of human mind, giving him the capacity to process more information, filtering the useless data. At least, my computer works for my well-being, saving a lot of time < that would have been spent reading badly written paragraphs. Computers are the most fascinating machines that was invented. Without it we would have less than we need to survive in modern society, which is controled by automation.
The first and most simple thought is the spark of a genius. The Turing Machine(TM) conceived by Alan Turing, in 1936, is an example of clarity of thought and the right ideas. A TM is like a K7 tape recorder. It has a finite tape, a header that goes forward and backward, a set of internal states, a set of inputs and outputs. The machine receives a program in the tape and as well as music, the tape is processed leaving the output written on it. The TM can be simulated using just pencil and paper. (all that the mathematical department needs to work), or simulated in a computer. The mathematical representation is given by $$M = (\Sigma^*,Q,I,O,q_0,\phi(\cdot))$$. A simple representation to capture the essence of computation.
Machines and Neurons
The human brain is the most intriguing part of nature's capacity to produce intelligence from mostly organic and mineral compounds. Without it art and science would be just noise and foolish words, without the brain the whole universe would be just a dark and forlorn place, our existence, just basic instinct. No emotions, and no feeling. As Galileo, the great astronomer, said the nature has all the solutions to simple and complex problems. And as the eagle flies precisely through the air, we have the brain. In the mid 20 century, the neuroscience met the computer, and the neuron had a electronic companion: the artificial neuron has a similar feature with the organic neuron, they possess the capacity to be excited not by nurotransmiters but by a mathematical numerical trigger. Using Lagrangean type of optimization, we can associate these neurons into layers and adding feedback circuits, we have an electronic brain. The applications range from classification problem solving, to visual processing, and machine's automation. A neural network can learn too, and using memory, can perform tasks as learning to play chess, and to make pattern recognition.
Programming Mahines
Operation Mapping