Article response: Trivium & Quadrivium

" Plato, …, conceived of such education as the sole occupation of the first thirty-five years of a man's life. He would have the first twenty years spent on gymnastics, music, and grammar, the next ten on arithmetic, geometry, astronomy, and harmony, and the next five on philosophy.1*"(p.264) 

I am interested in the subjects involved in the Greek educational system. These subjects are gymnastics, music, drawing, reading, writing, grammar, rhetoric, arithmetic, geometry, astronomy, natural sciences, harmony, philosophy, and dialectic. I have been thinking the similar thing. I suggest psychology and logic as essential studies for the modern world. We need to understand how people's brain is working, and how to think logically. These two points are important and useful.

I agree with Plato that ideally, people should have their first 30 or 35 years focusing on learning different types of subjects. However, not everyone can have such treatment. In ancient Greece, women were generally not given a formal education. Nowadays, obtaining education is a luxury for many people in the world. I am sad about this. I hope everyone could get the chance to go to school, go to university.

"Among the Greeks computation or reckoning, the arithmetic of business was called logistic and was considered to be entirely different from the study of number as such, which philosophical study was called arithmetic."(p.266)

The philosophical study was called arithmetic. This reminds me of Zeno's Dichotomy paradox and Achilles and the tortoise paradox. These paradoxes are a set of philosophical problems, but they are also mathematical mysteries. In ancient Greece, mathematics, astronomy, and philosophy are three subjects bundled together. I just wonder why we don't learn astronomy anymore. I still can remember how excited I was when my high school organized an event at an astronomical observatory. I think that learning astronomy could make the students curious and become more open. Ancient people like to gaze at the night sky, and modern people like to gaze at the cell phone screen. Although our brain can reach everything through this little screen, our heart is placed in a box, I mean we cannot feel those feelings.

P.273

It makes sense that the symbol of multiplication X is derived from above method. I think the solution is : 100 - 20 - 30 + 6 = 56. I wonder what if 3 x 7?   Using Recorde's method, (10-3 = 7 ) and (10-7=3 ), 3 x 7 =? It will go back to the original question. I think solution is : 10-3 = 7, then 100 - 70 - (10 - 7)x3 = 21. 

4 x 9 's solution: 10 - 4 = 6 , then 100 - 60 - (10-9)x4=36