Harmony in Architecture and Harmony in Physics

During the Renaissance period, Italian architects were interested in constructing useful buildings by combining Greek and Romanesque styles. The aesthetic value of Greek style was well appreciated. Romans figured out vector division of forces and were able to build domes and arches without supporting poles in the middle.

Yes, the first step to this approach would be to construct rotundas, with Greek columns and Roman roofs. Indeed, Italians built many rotundas in and near the city of Vicenza not far from Venice. Thomas Jefferson of the United States was a talented architect and reproduced this idea to build his own villa in this Renaissance style. The Thomas Jefferson Memorial in Washington, built in 1937, is an exact copy of his villa in Charlottesville (Virginia). Here are detailed views of this memorial.

Jefferson Memorial (front view)
(side view)
(rear view)

Let us go back to Italy. The Renaissance artists started with this simple combination. The person who created this new trend was Andrea Palladio. I went to Vicenza (Italy) during the last week of May (2008) to learn how Palladio was so creative. He did not invent his Palladio style overnight. He gradually developed his creativity from the simple idea of rotunda to his masterpiece called Teotro Olympica. This photo is from one of the guidebooks for the Veneto region.

More about Palladium Architecture

In looking at artworks, each individual has his/her own subjective way influenced by his/her cultural background. It was very clear to me that Palladio's main concern was how to achieve a "harmony" between the Greek and Roman traditions.

We say Pablo Picasso was a great artist. Why? If we look at a beautiful woman, we appreciate God's ability to combine eyes, lips, nose, and others in a harmonious manner. Picasso wanted to create his own harmony. He divided up all those components and then put them into different places to create his own harmony.

I seem to emphasize the "harmony" as an important variable in architecture (it is an important variable in music). Does this have anything to do with my Korean background? Perhaps Yes. Perhaps No. In either case, let us look at a couple of photos of Korean architecture.

Korean Architecture. Harmony with nature.
Another Photo.

Unlike those European cathedrals, Korean houses and buildings do not stand out. It is very difficult to extract artistic values from them. Right? Wrong! The strength of Korean architecture is its harmony with nature. I can of course talk more about its historical origin, but let me stop here.

How about harmony in physics? Whenever there is a great breakthrough, it is accompanied by a harmonious union of two or more existing disciplines.

Newton was able to combine comets (open orbits) and planets (bound orbits) into one equation of motion.

Einstein's
Observation
Galilean

Lorentzian

Newtonian
Mechanics
Yes

No

Maxwell's
E & M
No

Yes

Maxwell was able to unify electricity and magnetism to formulate electomagnetism, responsible for today's wireless world.
Einstein observed this mismatch between mechanics and electromagnetism and fixed the problem to formulate the principle of relativity
Heisenberg came up with his uncertainty priciple in an attempt to achieve a harmony between the particle nature and wave nature of matter.
How about Feynman? He believed in "one physics."
1. Click here for details.
2. Another webpage about Feynman.

The two greatest theories formulated in the 20th century are relativity and quantum mechanics. They were developed separately. It is a great challenge to see whether they can be combined harmoniously into one theory. Of course, the present form of quantum field theory is a great step toward solving comet (scattering) problems. For planets (bound-state), we have to take into account boundary conditions in a Lorentz-covariant manner, and the problem becomes more complicated. However, we can consider a harmonious union of Dirac's approaches to this problem.

Click here to magnify this figure.

The first step could be to translate both quantum mechanics and relativity into pictures.

In 1927, Paul A. M. Dirac noted there is an uncertainty relation between the time and energy variables, in addition to Heisenberg's position-momentum uncertainty relation. Dirac noted further that there are no excitations along the time axis.
In 1949, Dirac proposed the light-cone coordinate system to study coordinate transformations for Einstein's special relativity. In this system a square becomes squeezed into a rectangle.
However, Dirac did not draw pictures of what he was doing. He thus assigned very interesting homework problems for us.
If we translate Dirac's observations, we end up with this figure. Click here for a detailed explanation. The picture drawing culture was introduced to physics by Wheeler and Feynman.

Indeed, pictures and their harmony constitute a very powerful language in creating physics, in the tradition of Andrea Palladio.

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