Pythagoras declared that ‘all is number’, and everything could be understood in terms of numbers. It is not always easy to fully grasp the underlying philosophy of Pythagoras’s insights. We can, however, explore one of his most famous theorems which still bears his name today, concerning the triangle and its many ramifications.
Vesica Piscis, which literally means “the bladder of a fish” in Latin, becames the core of all solids. Image from Wikipedia.
According to Plato, the circle and the interaction of two circles, where the center of each circle lies on the circumference of the other (the so-called Vesica Piscis), became the core of all solids. Following this train of thought, geometry becomes music, and music becomes cosmic harmony and the music of the spheres.
Vesica Piscis with figures within. Image from dcsymbols.com.
It has been seen, however, that Pythagoras’s view, “all is numbers,” did not fully complying with the numbers which have been found at the time. Pythagoras himself only aware about rational numbers. So in Pythagoras time, numbers meant rational numbers. When Pythagoras and his students claimed that all things are numbers, they meant to imply that everything could be understood in terms of rational numbers. But, unfortunately, they soon discovered the irrational numbers which is, roughly speaking, inspired from by the phenomenon of the diagonal of a unit square. Pythagoreans discovered that the diagonal of a unit square, , is not commensurable with its side. And this has given the area to be solved in other fashion, such as arithmetic or algebraic fashion. So that mathematics, particularly number theory, has been growing and developing with fascinating discoveries as we have seen today.
On the sipirit of ‘sacred teaching’ of Pythagoras, whatever numbers we actually do or attempt to discover, or just seek another method of its approximation and representation, let’s see and do not bother with this funny comic. This maybe make us smile for today :
Comic : Number line by Jeff at xkcd.com
When we talk about humanities, I have a different opinion. I go for the opposite direction : what does it mean for everything? In fact, we can not mean or measure something unless it accounts any fraction of mathematics, and thus with numbers. But is there some other areas that can not be understood in term of numbers?
How about humanities? There is sensitive area when we talk about humanities or judge on the human values. The values of human beings are not only numbers, there are cultural minds that would be differs, such as theoritic values, economic values, solidarity values, politic values, religious values and artistic values. The values are there in all people, differ from one person to another, between one society to another and between cultures with each other, not in quantity, but on the configuration of these values.
So, when we talk about humanities and the human values, it is not appropriate to measure these values with only positivist method of calculating or measuring with the set of numbers. Because humans have soul arrangements which is called cultural mind, which created the culture and living in a culture. Maybe, for this kind of values, we have to use another method, such as understanding method (Verstehen) instead of using positivist method of calculating and measuring.
Note : I just wrote this post in a few minutes, and attached the comic for fun without any tendency. I hope you enjoy as well as I enjoy the humor in my life. 🙂