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Benvenuti in queste pagine dedicate a scienza, storia ed arte. Amelia Carolina Sparavigna, Torino

Wednesday, January 4, 2012

A "Noah's ark" rock

Mount Ararat is a volcanic structure, having two peaks: the Greater Ararat with an elevation of 5,137 m and  Lesser Ararat with an elevation of 3,896 m. The Ararat massif is about 40 km  in diameter. Traditionally, Mount Ararat is associated with the Mountains of Ararat, where according to the book of Genesis,  Noah's ark came to rest. In Wikipedia, "The Bible says that Noah's ark landed on the mountains of Ararat. This does not refer to any specific mountain or peak, but rather to a mountain range within the region of Ararat, which was the name of an ancient proto-Armenian kingdom also known as Urartu.... Ararat is a stratovolcano, formed of lava flows and pyroclastic ejecta, with no volcanic crater. Above the height of 4,100 m, the mountain mostly consists of igneous rocks covered by an ice cap. A smaller 3,896 m  cone, Little Ararat, rises from the same base, southeast of the main peak. The lava plateau stretches out between the two pinnacles. .... It is not known when the last eruption of Ararat occurred; there are no historic or recent observations of large-scale activity recorded. ... It seems that Ararat was active in the 3rd millennium BC; under the pyroclastic flows, artifacts from the early Bronze Age and remains of human bodies have been found."

Using the satellite maps, I was searching for any stone structure in the Ararat area, made by ancient men, as I  did in Arabia and Syrian Desert [1,2], when I saw what looks like a huge rock structure, broken in two parts. This natural structure has a color and outline quite different from the surrounding area. Since it is on Ararat, let me call it the "Noah's ark" rock!


Genesis 6:15, English Standard Version (ESV)
This is how you are to make it: the length of the ark 300 cubits,
its breadth 50 cubits, and its height 30 cubits.



To see some ancient man-made stone structures, please visit: 
Arabia: from craters to stone circles,  http://www.archaeogate.org/classica/article/1327/1/arabia-from-craters-to-stone-circles-di-amelia-carolina.html
Stone structures in the Syrian Desert , http://www.archaeogate.org/vicino_oriente/article.php?id=1445

Tuesday, January 3, 2012

An Arctic solution to the data storage

Cold storage - an Arctic solution to the data storage cooling problem | In-depth | The Engineer
"We generate a storm of data throughout the day, whether we want to or not ... And the amount of data we generate personally is dwarfed by the numbers generated by government, industry and commerce. All this data has to be stored and this is giving rise to a new form of building, characteristic to the early 21st century: the data centre. Sharing some of the form and characteristics of ages-old strongrooms and more modern hardened bunkers, these are the locations that keep the numbers vital to our lifestyles, and the fortunes of government and industry, safe. But this has also generated a set of problems for civil engineers. The most vital thing that a data centre has to do is to keep its ranks of computer servers running. For that, they need two things: power and cooling..."

Cloaking objects from surface water waves

Viewpoint: Cloaking Comes Out of the Shadows, by Ross McPhedran, Alexander Movchan.
http://physics.aps.org/articles/v5/2
"Cloaking devices made of a composite of soft and hard materials can divert elastic vibrational waves around an object as though it wasn’t there. Though cloaking devices are mainly associated with hiding objects from light, the concept of cloaking is not restricted to electromagnetic waves. Experimentalists have shown they can cloak objects from surface water waves [1] and electron waves on the surface of metals (plasmons) [2]. Now, Nicolas Stenger at the Karlsruhe Institute of Technology in Germany and his colleagues have designed and tested a cloak that makes an object in a flexible medium invisible to elastic vibrational waves [3]; that is, the waves pass by the object as though it wasn’t there. The work, which is presented in Physical Review Letters, describes a cloaking device that is both more efficient and covers a wider bandwidth than any other existing cloak."

Aristippus of Cyrene

from THE ARCHITECTURE, by MARCUS VITRUVIUS POLLIO.
BOOK THE SIXTH, INTRODUCTION.

ARISTIPPUS, the Socratic philosopher, shipwrecked on  the coast of Rhodes, perceiving some geometrical diagrams thereon, is reported to have exclaimed to his companions, " Be of good courage, I see marks of  civilization" and  straightway making for the city of  Rhodes, he arrived at the Gymnasium; where, disputing on philosophical subjects, he obtained such honours, that he not only provided for himself, but furnished clothing and food to his companions. When his companions had completed their arrangements for returning home, and asked what message he wished to send to his friends, he desired them to say that the possessions and provision to be made for children should be those which can be preserved in case of shipwreck; inasmuch as those things are the real supports of life which the chances of fortune, the changes of public affairs, and the devastation of war, cannot injure.

Monday, January 2, 2012

2011: The Year of Materials

Vibrant displays head to market, invisibility cloaks become more practical, and batteries store more energy...
The Year in Materials - Technology Review

Thursday, December 29, 2011

A mound near Jefferson City

"Before the coming of white settlers, the region surrounding Jefferson City was home to an ancient group known as the Mound People. In fact, America's largest prehistoric city was located only 160 miles away at what is now Cahokia, Illinois. Why this civilization disappeared remains a mystery."
http://www.jeffcitymo.org/main/historyheritage.html
Information on the mounds near Jefferson City we can find in the paper
published by The Project Gutenberg EBook of Scientific American Supplement, No. 841,
February 13, 1892, by Various
INVESTIGATION OF A MOUND NEAR JEFFERSON CITY, MO, By A.S. LOGAN.
Logan wrote
"Recently, a party consisting of engineers and employes of the Missouri River Improvement Commission began an exploration of one of the mounds, a work of a prehistoric race, situated on the bluff, which overlooks the Missouri River from an elevation of one hundred and fifty feet, located about six miles below Jefferson City.
This mound is one of about twenty embraced in a circle one quarter of a mile in diameter.
The above party selected the mound in question apparently at haphazard; all the mounds presenting nearly a uniform outline, differing only in size and mostly circular in form, and from twenty to twenty-four feet at the base, rising to a height of eight feet and under. A trench was cut on a level with the natural soil, penetrating the mound about eight feet. A stone wall was encountered which was built very substantially, making access in that direction difficult, in consequence of which the earth was removed from the top for the purpose of entering from that direction. The earth was removed for a depth of four feet, when the top of the wall was exposed. Further excavation brought to light human bones, some of them fairly well preserved, especially the bones of the legs. On the removal of these and a layer of clay, another layer of bones was exposed, but presenting a different appearance than the first, having evidently been burned or charred, a considerable quantity of charcoal being mixed with the bones. In this tier were found portions of several skulls, lying close together, as if they had been interred without regard to order. They were, in all probability, detached from the body when buried....
A few pieces of flint weapons were found in the upper layers, and nothing else of any significance....
At this juncture the diggers abandoned the search, and some days later the writer, desirous of seeing all that was to be seen, resumed the work and removed the earth and remains until the bottom of the vault was reached; several layers being thus removed. All of these had evidently been burned, as charcoal and ashes were mixed with the bones of each succeeding layer. The layers were about an inch in thickness, with from two to four inches of earth between, and small flat stones, about the size of a man's hand, spread on each different layer, as if to mark its division from the next above.
Between the bottom layers, mixed with charcoal, ashes and small portions of burned bones were found what gives value to the search, numbering about fifty tools and a smoking pipe.
The material of the tools is the same as the rock forming the vault, locally known as "cotton rock." I would consider it a species of sandstone.
Overlying the edge of "cotton rock" in the bluff is flint in great quantities, and in every conceivable shape, that these people could have resorted to had they been so disposed, and why they used the softer material I will leave to some archæologist to determine. The tools themselves are made after no pattern, but selected for their cutting qualities, as they all have a more or less keen edge which could be used for cutting purposes, and were no doubt highly prized, as they were found all in a pile in one corner of the vault and on top of which was found a stone pipe. The pipe is made bowl and stem together, and it is curious that people of such crude ideas of tools and weapons should manufacture such a perfect specimen of a pipe. It is composed of a very heavy stone, the nature of which would be difficult to determine, as it is considerably burned.
A description of the vault will be found interesting to many. The wall of the vault rests upon the natural surface of the ground, about three feet high and eight and a half feet square, the inside corners being slightly rounded; it is built in layers about four inches in thickness and varying in length upward to three feet, neither cement nor mortar being used in the joints; the corners formed a sort of recess as they were drawn inward to the top, in which many of the stones were found. The stone for constructing the vault was brought from a distance of about a quarter of a mile, as there is none in sight nearer.
I assume from all these circumstances that these people lived in this neighborhood anterior to the age of flint tools, as the more recent interments indicate that they were then entering upon the flint industry, and it may be that the "cotton rock" had become obsolete.
These people buried their dead on the highest ground, covering and protecting them with these great mounds, when it would seem much easier to bury as at the present day; but instead, they, with great labor, carried the rock from a great distance, and it is reasonable to suppose, also, that the earth was brought from a distance with which they are surrounded, and piled high above, as there is no trace of an immediate or local excavation....
My object is the hope of a more thorough investigation at some future time...."

Wednesday, December 28, 2011

Bicycles - 1897

From
The Project Gutenberg EBook of The Great Round World and What Is Going On
In It, Vol. 1, No. 19, March 18, 1897, by Various

INVENTION AND DISCOVERY

Some lover of the wheel, who evidently cannot bear to lose the pleasure of wheeling even when the snow lies thick on the ground, has invented a sleigh attachment. This is a runner fastened beneath the driving-wheel of the bicycle. 





What a great thing this will be! Fancy wheeling away over the snow, propelling our wheels as fast as the pedals can make us go. The bicyclists ought to be very happy this year; so many clever brains are working for their comfort and pleasure. All who ride have been troubled at times what to do with the bicycles when they are standing still.


It may be there is damp grass, which would make it impossible to lay the precious wheel down; or there may be a thousand other little inconveniences. Some one has come to the aid of the bicyclist, and invented a bicycle support, which can be secured to the machine, and raised at will, so as not to interfere with the wheel when in motion. It is just the thing all bicyclists have been longing for.



Another busy brain has been at work in anticipation of the summer, and the glorious time in store, riding along the country roads. An umbrella support is the result. It consists of an attachment composed of portions which can be connected or removed at will. What a boon it will be, on a hot summer's day, to have an umbrella comfortably held over one's head, while the hands are free to guide the wheel!

The searchlight - 1897

The Project Gutenberg EBook of The Great Round World and What Is Going On
In It, Vol. 1, No. 15, February 18, 1897, by Various
http://www.gutenberg.org/files/15325/15325-h/15325-h.htm
we find the following news

"INVENTION AND DISCOVERY.- 1897
A New York newspaper has been making some experiments in signalling ships at night, which, if as successful as it is claimed to be, will be of the greatest service to sailors for all time to come.
Ships have a regular way of talking to one another, by means of flags arranged in certain ways...
There has been one difficulty with the flag-signals, and that has been that they were useless at night. When it became too dark for the flags to be seen, sailors had no other means of communication.
The New York paper claims to have overcome this difficulty.
In saying that ships have no means of communicating with each other, it must not be forgotten that they can use lights and send certain messages with them. But the flag system enables them to say exactly what they wish to, while through the lights they can only show where they are, and call for help in case of accident.
The invention of the searchlight set men thinking, and at last the idea struck one man that if the searchlight were turned on the flags, it ought to be perfectly possible to see them in the darkest night.
A few nights ago two tugs went down to Sandy Hook to try if the experiment would work. To their great delight they found it did answer perfectly. The tugs were stationed about a mile and a half apart, and could read with ease the messages waved across the water.
More experiments will be made, and if on further trial the method is found to be practical, a great advance will have been made in navigation...
This invention is in the nature of a powerful foghorn. It is, however, made somewhat like a musical instrument, so that different tones can be produced by it; and the idea is to have these tones arranged into a signalling code, after the fashion of the flag-signals, so that a conversation can be kept up in a similar way to that done with flags. G.H.R."


Edison's searchlight cart, from the Smitsonian: http://americanhistory.si.edu/edison/ed_d21.htm

Of course, the use of the Morse Code is better. But we have to wait till the Aldis Lamp.
According to the Oxford Dictionary: Aldis lamp, a handheld lamp for signalling in Morse code. Origin:
First World War: named after Arthur C. W. Aldis (1878–1953), its British inventor
The Aldis Lamp is a  signal lamp, a visual signaling device for optical communication (typically using Morse code). Modern signal lamps are a focused lamp which can produce a pulse of light.


Moving sand dunes

 In several desert areas, the slow motion of sand dunes can be a challenge for modern human activities and a threat for the survival of ancient places or archaeological sites. However, several methods exist for surveying the dune fields and estimate their migration rate. Among these methods, the use of satellite images, in particular of those freely available on the World Wide Web, is a convenient resource for the planning of future human settlements and activities. More at http://arxiv.org/abs/1112.5572




The barchans move. Note the dunes on the tracks.

Centennial Superconductivity

The Japanese Journal of Applied Physics
Volume 51, Number 1, January 2012
had published the Special Section: Centennial Anniversary of Superconductivity in commemoration of the 50th anniversary of JJAP and the centennial anniversary of superconductivity.

Special Section —Centennial Anniversary of Superconductivity—
Comprehensive Review
Invited Review Papers
Selected Topics in Applied Physics
Rapid Communications
Regular Papers
Semiconductors, dielectrics, and organic materials
Photonics, quantum electronics, optics, and spectroscopy
Spintronics, superconductivity, and strongly correlated materials
Device physics
Nanoscale science and technology
Crystal growth, surfaces, interfaces, thin films, and bulk materials
Plasmas, applied atomic and molecular physics, and applied nuclear physics
Device processing, fabrication and measurement technologies, and instrumentation
Brief Notes

Tuesday, December 13, 2011

Higgs boson

"On Tuesday, physicists at the Large Hadron Collider near Geneva, Switzerland, said that data from two independent experiments had helped them narrow the range of what the mass of the Higgs boson could be. Higgs bosons—if they exist—are created in the giant atom-smashing machine, where they almost instantly decay into other particles. Discovery is based on observing the particles into which they decay.
One experiment, known as Atlas, suggested that the hypothesized Higgs is most likely to have a tiny mass, in the range of 116 to 130 gigaelectronvolts, or GeV. The other experiment pegged mass at 115 to 127 GeV. The experiments were carried out at the European particle physics laboratory CERN near Geneva."
http://online.wsj.com/article/SB10001424052970203430404577096330121408786.html
Wall Street Journal

Thursday, December 8, 2011

Acoustic freezer

Thermoacoustic engines (sometimes called "TA engines") are thermoacoustic devices which use high-amplitude sound waves to pump heat from one place to another, or conversely use a heat difference to induce high-amplitude sound waves. In general, thermoacoustic engines can be divided into standing wave and travelling wave devices. These two types of thermoacoustics devices can again be divided into two thermodynamic classes, a prime mover (or simply heat engine), and a heat pump. The prime mover creates work using heat, whereas a heat pump creates or moves heat using work. Compared to vapor refrigerators, thermoacoustic refrigerators have no ozone-depleting or toxic coolant and few or no moving parts therefore require no dynamic sealing or lubrication.
More http://en.wikipedia.org/wiki/Thermoacoustic_heat_engine

Wednesday, December 7, 2011

Mollusc shell features in engineering materials

"The mollusc shell is made up of only one mineral: calcium carbonate, yet the combination of that plus other enzymes and proteins gives it remarkable properties in terms of strength, while remaining incredibly light. Prof Mark Rodger, project leader and director of Warwick University’s Centre for Scientific Computing, told The Engineer: ‘The whole point of this project is to try to understand what happens when you make hybrid materials that are partly organic and partly inorganic.’"

Read more: Mollusc shell features could be replicated in synthetic fabrics | News | The Engineer

Monday, December 5, 2011

Hic sunt Garamantes

"Satellites and aerial photographs have revealed evidence of over a hundred fortified farms, villages, and towns - many with castle-like structures - in the southwestern deserts of Libya. These structures date back to between 1 and 500 C.E., meaning they predate the rise of Islam. ...
Archaeologists from the University of Leicester have used all this aerial data to identify as much as they can about the so-called Garamantes people, who are otherwise known purely through Greek and Roman sources. They've already discovered "the mud brick remains of the castle-like complexes, with walls still standing up to four metres high, along with traces of dwellings, cairn cemeteries, associated field systems, wells and sophisticated irrigation systems." "
http://io9.com/5857958/satellites-reveal-libyas-lost-2000+year+old-cities

Friday, December 2, 2011

Raphael's portrait of Leonardo

Published as An image processing of a Raphael's portrait of Leonardo, by Amelia Carolina Sparavigna, Dipartimento di Fisica, Politecnico di Torino, http://arxiv.org/abs/1111.6030
Abstract: In one of his paintings, the School of Athens, Raphael is depicting Leonardo da Vinci as the philosopher Plato. Some image processing tools can help us in comparing this portrait with two Leonardo’s portraits, considered as self-portraits.

The "Scuola di Atene" is one of the most famous paintings by Raphael, the Italian Renaissance artist. Painted between 1510 and 1511, this fresco decorates the wall of one of the rooms, the "Stanza della Segnatura", in the Apostolic Palaces of Vatican. The great Greek philosophers are represented inside a classic architecture. At the central position of this masterpiece, we see two philosophers, Plato on the left and Aristotle, his student, on the right. Plato is shown as a wise-looking man (see Fig.1). It is believed that Raphael based the Plato's face on the features of Leonardo da Vinci [1]. The two artists probably had established a direct interaction when Raphael spent a period of his life in Florence, perhaps from about 1504 to 1508 [2-4]. Leonardo da Vinci returned to Florence from 1500 to 1506: therefore, if the image of Plato is a portrait of Leonardo, this means that Raphael depicted him when Leonardo was 52 or 54 year old.  

Fig.1 Raphael’s Plato (image source: http://www.aiwaz.net/)
To see a slide-show of Raphael's masterpieces, visit please https://www.artsy.net/artist/raphael

There is a portrait in red chalk, dated approximately 1510 and held at the Biblioteca Reale of Turin, which is widely accepted as a self-portrait of Leonardo da Vinci. It is thought that Leonardo drew this self-portrait at the age of 58 or 60 (see Fig.2). Ref.5 tells that this well-known drawing is not universally accepted as a self-portrait, because the depicted face appears to be quite old, suggesting that Leonardo represented his father or grandfather. Another possibility is that Leonardo altered himself, in order that Raphael might use it for his Plato. However, Plato does not look so old in the painting by Raphael.

Fig.2 Leonardo’s portrait in red chalk (dated approx. 1510) held at the Biblioteca Reale of Turin.

In any case, let us try to find some matching points between the portraits, that of the man in red chalk (Fig.2) - let us call it from now on the self-portrait in red chalk – and the image of Plato (Fig.1) that Raphael had depicted in his fresco. To match the two faces, the image processing is fundamental: in particular, we will use another Leonardo's portrait merged with the self-portrait in red chalk. This portrait is a drawing of the Codex on the Flight of Birds, which Leonardo had partially hidden by his writing, as shown in Fig3, left panel. According to Carlo Pedretti, an Italian historian expert on the life and works of Leonardo, this is a self-portrait [6,7] made when the artist was young. The codex dated approximately 1505, but the portrait is older for sure: Leonardo recycled the paper for the composition of the Codex.
To use this portrait it is necessary to remove the written text. Carlo Pedretti was the first to suggest a “restoration” of this drawing, of course not of the real page of the Codex, but made on a photographic plate. It was only two years ago, in 2009, that Piero Angela, an Italian scientific journalist, presented the digital restoration of the portrait [8,9], that is, the restoration of the corresponding digital image. In 2009, I have proposed a simple approach that uses an iterative procedure based on thresholding and interpolation with nearest neighbouring pixels [10,11]. Recently, I proposed a further processing with a wavelet-filtering program, Iris [12-14]: the result is shown in Fig.3, right panel. According to Pedretti, this is the young Leonardo da Vinci self-portrait.
Fig.3. A page of the Codex on the Flight of Birds contains a Leonardo’s portrait. Using a digital restoration that removes the writing, the portrait appears.

For any comparison with the Raphael’s portrait, we have to complete this image, since the artist abandoned it unfinished. We use another processing tool, the GIMP [15], for this purpose. Using GIMP, we can add this drawing of the young man to the self-portrait in red chalk of the old man. The result is given in Fig.4: besides showing that the two faces have the same relative distances of eyes, nose and mouth, this portrait makes the old Leonardo look younger.


Fig.4 Using GIMP [15] we can add the portrait of the young man (Fig.3, right) to the self-portrait in red chalk (Fig.2) of the old man.

Fig.5 On the right, the Raphael painting and on the left, the result of a merging of two Leonardo’s drawings

In Figure 5 we have the two images, the Raphael painting on the right and the result of merging the two Leonardo’s drawings on the left, shown side by side. Let me remark that we are looking at two images obtained from originals created by two artists who used different techniques and a different rendering of the head position. Moreover, there is another fact, which is in my opinion quite important, that the two portraits are showing a distinct side of the face. And we know very well that the two sides are not equal and that the existing small differences create the "good" and "bad" side of our faces [16].
Let us remember that for all the living creatures, the bilateral symmetry [17] of the body is an approximate symmetry: the two halves, left and right, of the body and then of the face, are not perfectly symmetrical. The symmetry of human faces is a subject of several studies. Some researchers are supporting the idea that more symmetry means more beauty and freedom from diseases [18-20]. On the other hand, a face, which is too symmetric, gives the impression of being unnatural [21].

Fig.6. Let us consider two canvasses, having on them a self-portrait and a portrait respectively, with the head depicted in the same position. The side of the face is different. When an artist is depicting a self-portrait, he is looking at the face in a mirror. Assuming the position of the head as above, the self-portrait is showing the left side of the face. In the case that it is another artist depicting the portrait, he is looking at the face directly, and then the side depicted is the right one.

The fact that the two sides are different is quite relevant if we are comparing a self-portrait with a portrait, because we must be sure to compare the same side of the face. For the explanation, let me use Fig.6. Let us consider two canvasses, having on them a self-portrait and a portrait, with the head depicted in the same position, the two paintings are showing a different side of the face. When the artist is depicting a self-portrait, he is looking at the face in a mirror. When it is another artist depicting the portrait, he is looking at the face directly. For this reason, if the face on the canvas has the same position, the depicted sides turn out to be different. Therefore, if the left image of Fig.5 is a self-portrait and the right image is a portrait, it is necessary to reflect one of then, to point out that we are seeing different sides.
I decided to change the Raphael’s image, with a reflection and a small rotation using GIMP. Moreover, I converted the colours in grey tones, to avoid the vision of different hues. Fig.7 gives the result. Is the figure showing the same person? I guess that there is this possibility, but further studies are necessary. Let me then avoid a direct answer and just write some conclusions.


Fig.7 Is this the same person?

Using the image processing we had compared portraits having quite different origins. This is telling that several processing tools, some of them freely available, can help in the study of history and arts. For what concerns the specific case, it seems from Fig.7, that the structure of the two faces, in particular of nose and cheekbones, is quite similar. We can also see that one of the eyes is a little bit larger in both images. According on the previous discussion on portrait and self-portrait (Fig.6), I tend to consider the Raphael’s Plato based on a direct interaction between Raphael and Leonardo, when Raphael was in Florence, and then on a previous portrait or drawing that Raphael made of Leonardo.

References
1. Raffaello Sanzio, presentato da M.G. Ciardi Dupré, Milano, Fratelli Fabbri Editore, 1963.
2. Cecil Gould,  The Sixteenth Century Italian Schools, National Gallery Catalogues, London 1975.
5. Cultural depictions of Leonardo da Vinci,
6.. E. Crispino, C. Pedretti, C. Frost, Leonardo: Art and Science,  Giunti, 2001. 
7. C. Pedretti, A Chronology of Leonardo Da Vinci's Architectural Studies after 1500, E. Droz, Geneva, 1962.
8. ANSA.it - News in English - Leonardo self- portrait 'discovered', 2009 and also BBC NEWS  Europe - 'Early Leonardo portrait' found, 2009.
10. Amelia Carolina Sparavigna, 2009, The Digital Restoration of Da Vinci's Sketches, http://arxiv.org/abs/0903.1448
11. Amelia Carolina Sparavigna, 2009, Digital Restoration of Ancient Papyri, http://arxiv.org/abs/0903.5045
12. Amelia Carolina Sparavigna, 2011, A self-portrait of young Leonardo, http://arxiv.org/abs/1111.4654
13. Iris © 1999-2010, Christian Buil, http://www.astrosurf.com/buil/us/iris/iris.htm
14. Amelia Carolina Sparavigna, 2009,  Enhancing the Google imagery using a wavelet filter, http://arxiv.org/abs/1009.1590
15. GIMP © 2001-2011, http://www.gimp.org/
16. I have read on the Glamour Magazine about a simple  experiment by P. Gugliemetti, Do You Have A Good Side And Bad Side Of Your Face?, 11-13-2008. The author writes "At a party over the summer, I mentioned to someone how I have a good side and bad side, and she thought I was just being dramatic. So I had her take a photo of each side and we showed the shots to random people in the room, asking them to vote on which side was my prettier one. Every single person voted right! Then we tried this on other people, lining them up one-by-one against a white wall, shooting their sides, and having people vote. Only a couple had equally attractive sides."
17. Bilateral symmetry of a body means that there exists a plane which is dividing the body into two mirror image halves. An operation of reflection shows that the two halves coincide.
18. G. Rhodes and L.A. Zebrowitz, Facial Attractiveness - Evolutionary, Cognitive, and Social Perspectives. Ablex. ISBN 1567506364, 2002
19. R.J. Edler,  Journal of Orthodontics Vol.28(2), pag.159, 2001
20. K. Grammer and R. Thornhill, Journal of Comparative Psychology, Vol. 108, pag.233, 1994.
21. R. Kowner, Journal of Experimental Psychology: Human Perception and Performance, Vol.22, pag.662, 1996.