TUNNELLING BETWEEN HISTORY OF PHYSICS AND ART
Budapest Tech, Hungary
How do the musical ratios of Pythagoras get into a Raphael’s painting, and how does the law of reflection find its way into Dante’s work?
They seem to be here and in many paintings and poems, as if a phenomenon or a law of physics appeared by tunnelling in another segment of culture. Using these emergences we can illustrate physical laws, helping better understanding. The history of physics offers an especially good possibility for this, because there we can show the connection between physics and the other areas of culture and in this way our students can get a more complete conception of the world.
In Raphael’s School of Athens ancient scientists bear the features of contemporary painters and architects. Aristotle and Plato are holding their works and we can recognize Leonardo da Vinci in the latter scientist. The architect Bramante is the face of the figure thought to be either Euclid or Archimedes. Pythagoras is explaining the musical ratios to a pupil, which is confirmed by the tablet in front of him. (Figure 1) It shows Greek words: at the top the word for tone, EPOGLOWN, the meanings of words diatessaron, diapente, diapason are: fourth, fifth and octave. The roman numerals for 6, 8, 9, and 12, show the ratio of the intervals producing harmonious sounds on a plucked string. On the tablet, under this depiction there is a triangular number 10. The ancient Greeks referred to it as the sacred tetractys, ten being the sum of the first four, very important numbers.
IV VIII VIIII XII
2 Illustrations from fine art and literature for chapters of physics
Fine art and literature offer an inexhaustible source of illustrations to the laws of physics. This talk presents such illustrations to help with the teaching of some selected chapters of physics, although we could fit examples of art into each chapter of physics. The historical overview of some topics of physics can be followed through by highlighted works of art of the same period of history. Examples of this kind will also be presented.
2.1 Physical and art-aspects of space and time
Following the history of physics and technology, we can find impressive illustrations to this topic.
The depictions of time and clocks reflect the level of physics in a given period of history.
On Holbein’s painting, The Ambassadors (dated 1533), on a shelf there are tools depicted with scientific precision, which show the exact time of the creation of the painting and also the temporal positioning of the Sun and the Moon, even the place of the topic of the painting. (Figure 2) 
The Pegwell Bay – a recollection of October 5th 1858, by William Dyce can represent the sum of knowledge about time and space in the middle of the 19th century. (Figure 3)
Here we can see an artist, looking at the passage of a comet, which was at its brightest on the mentioned day. This means the astronomical time. The cliffs, which have evolved over millions of years, and the collected shells and rocks talk about the geological time. The people who collect them symbolize the daily time and a very different timescale. So the comet and the cliff illustrate the vastness of space and time, and in contrast with this, the artist shows the other scale: the possible space for the observer by the effect of perspective and the relative short human life. 
Let me show an interesting sundial from the 20th century. The Hungarian artist, István Orosz created My Sun and your Sun. (Figure 4) The old device to measure time seems to be connected with the pair of concepts, space and time, which became important, but somehow confused images in the 20th century.
2.2 The laws of optics on paintings and in poems
In the Dewdrop by Escher both reflection and refraction can be recognized in the dewdrop itself, which behaves like an optical lens. (Figure 5)
We can also come across the law of reflection in Dante’s Divine Comedy:
“As when from off the water, of a mirror,
The sunbeam leaps unto the opposite side,
Ascending upward in the selfsame measure
That it descend, and deviates as far
From falling of a stone in line direct,
(As demonstrate experiment and art,)”
(Purgatorio XV. translated by H. W. Longfellow)
2.3 The camera obscura in the history of physics and in the arts
It was Aristotle who first mentioned the camera obscura-type effect in connection with a solar eclipse. Leonardo da Vinci mentioned this device as “the means of studying colour and coloured shadow”. Kepler completed it with lenses and later he painted a landscape using camera obscura. Descartes also experimented with it.
Constantin Huygens had a camera obscura. He was Christian Huygens’ father, otherwise poet and composer, played on several musical instruments and created more than 700 musical compositions. He studied mathematics and read law, and knew Descartes and Rembrandt. He spoke highly of the camera obscura in his poem, The daily work:
Vermeer, the Dutch painter, who was Huygens’ contemporary, probably used a special type of camera obscura, to create his paintings.
Looking at Vermeer’s The soldier and the laughing girl, we can recognize the use of the camera obscura, because the difference in size between the soldier, sitting near us, and the girl, who is not too far from us, is characteristic of a photograph rather than of a contemporary painting. (Figure 6)
2.4 Duality and Complementarity Here and There – Everywhere
What is light? A simple small poem about the frog can be used to demonstrate the wave-particle duality of light:
“It swims: a fish’s feature,
It jumps: a sparrow’s act,
Frog ‘s the name of this creature,
No kidding, it ‘s a fact.”
Similarly to the frog: light can behave in different ways, sometimes as a wave and sometimes as a particle. In fact it is neither wave, nor particle, but – light.
Perhaps we can illustrate the model above by a picture by Escher, Verbum, where we can find all three of the animals in their own vital conditions, and the animals in daytime and night time are complementary in several aspects. (Figure 7) In such a way we can emphasize the relationship of duality and complementarity.
Similar associations came to my mind, when I read the following lines from Shakespeare’s Hamlet of a conversation between Hamlet and Polonius:
“Hamlet: Do you see yonder cloud that ’s almost in shape of a camel?
Polonius: By the mass, and ’t is like a camel indeed.
Hamlet: Methinks it is like a weasel.
Polonius: It is backed like a weasel.
Hamlet: Or, like a whale?
Polonius: Very like a whale.”
Similarly, as a cloud can appear in the shape of a camel, or a weasel, perhaps a whale, light (electromagnetic radiation) can behave like transversal wave on a rope, or a collection of small balls. In reality some characteristics of the mentioned animals and things, under certain conditions, can describe the behavior of the cloud, or of light respectively.
2.5 Association between a picture and the special theory of relativity
What is the real topic of Istvan Orosz’ Jules Verne Anamorphosis: is it a landscape or a portrait of Verne? (Figure 8) Looking from different perspectives (from different frames of reference) there are different answers. On the flat surface we see a landscape, but on the surface of a cylindrical mirroring object a portrait appears.  In this way the above mentioned question is wrong, just like in the well known example of the special relativity: what is the real lifetime of the muon? The average lifetime of a muon in a laboratory system is about 2,2∙10-6 s. If the muon is moving towards the earth at a speed of 0,999c, then from the earth’s frame of reference the lifetime of the muon is about 22 times longer. So the question about its real lifetime is meaningless.
3 Conclusion drawn from a different aspect
Highly educated people are expected to have some scientific knowledge. Similarly, if we want to train well educated teachers, physicists or engineers, their knowledge of art and literature is also important to some extent. The above mentioned types of illustrations are suitable for arousing our students’ interest.
 North J 2005 The Ambassadors’ Secret (Hung. ed. Typotex, Budapest)
 Lippincott K 2002 The Story of Time (Hung. ed. Perfekt, Budapest)
 Orosz I 2006 Clouds for Polonius (Ernst Múzeum, Budapest)
A version of this article was presented at the GIREP-EPEC Conference “Frontiers of Physics Edycation” Opatisa, Croatia, 2007.