### a strange beauty

Can a math equation or a physical theory be beautiful?

By Gabriel Ferrero

The story goes that once somebody asked Einstein what he would think if it was discovered that the theory of relativity - one of his great contributions to science - was incorrect. Apparently, the great physicist answered that in this case “God lost the opportunity to do something really beautiful”. He obviously had no self-esteem troubles. But the adjective “beautiful” can be even more striking.

Many people, legions of high school students among them, often ask themselves how somebody can love and even consider math equations or physical theories beautiful. Curiously enough, though, it is quite common to hear a mathematician say that a theorem has a “very elegant” demonstration, or a physicist praise “the beauty” of a theory. I myself have often rejected the solution I have found for a physical-mathematical problem because I found it “ugly”.

What lies behind these statements? Perhaps an example could come in handy so that we can understand one another. I will copy Maxwell’s equations for the electromagnetic field. I know that many readers will have probably skipped this page at the mere sight of such formulas, but if you made it so far and didn’t study physics, I’ll let you into a little secret I learned reading Penrose: don’t worry about understanding them. Not even we physicists are sure about what they really represent.

Let’s take note of something which might not stand out at first sight: their simplicity. They are only four equations and contain but twelve symbols, eight of which represent math operations and four, physical magnitudes. For instance, “t” stands for time.

The amazing thing is that these equations are enough to describe, explain and predict a huge amount of phenomenon, among them: light, ultraviolet radiation, infrared radiation, X-rays, radio waves and the way each one of these spread through space, through time, throughout the entire universe. With some additional term, these equations also enable the invention, design and construction of many useful things: electric engines, antenna, loudspeakers, microphones, radios and radio receivers, tinted glass, microwave ovens, 3D movies, etc. The list is probably endless.

Using only twelve symbols, arranged in four equations, we understand countless phenomenon… Isn’t it marvelous? It is a magnificent synthesis! And if we think about the variety, the complexity and the extension of what they represent, we can partly understand why we say that equations are very simple.

Of course it is necessary to study a bit, perhaps more than a bit, in order to understand them, but we can all see that they are very brief, concise and have a limited and really small number of operations. Yet another example of their simplicity.

On the other hand, let’s look at the first and third equations. We can see that if we change symbol E, which represents the electric field, with B, which represents the magnetic field, the equations are the same. Likewise, the second and fourth are very similar. That’s why we say that there’s a certain symmetry in the equations. By interchanging some symbols, the equations become the other, totally or partially, but we always maintain, almost, the same group of equations.

This symmetry of the equations expresses something very deep about the nature of electricity and magnetism. In a way, each one of these phenomenon is the consequence of the other. One could say they express something, a fundamental property of matter which manifests itself in very different ways, yet symmetrical. That is also why we say that equations are beautiful. Simplicity and symmetry: two attributes that make what we call beauty.

Some months ago a colleague showed me a scientific article he had just written. In it he described the behavior of an electron inside a certain molecule under certain conditions in full detail and precision. The corresponding equations took up several pages crammed with symbols which were very hard to understand. I confess I couldn’t avoid saying: how beautiful!

There is also beauty in complexity, when simplicity or symmetries aren’t that obvious. In order to write that equation my friend had to find the way of expressing mathematically, in a clear and explicit way, the relation of each electron with several atomic nuclei, with other electrons, with other molecules, with the electric and magnetic fields present in the matter… in sum, a large number of relations. I think the beauty we perceive in complex phenomenon are related to the beauty of relationality, with something deeply constitutive of what is real, of that which exists.

Everything, from the most basic and elemental levels of matter, exists in relation to, is related to, further still, everything is itself only in relation to others. Perhaps this is the most typical beauty of our times.

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### how did buddha influence the world?

Buddha established a new religion which changed many societies. Already around 300 BC Buddhism gained political influence. Indian emperor Ashoka the Great established a Buddhist kingdom and based his reign on the Buddhists precepts.
Life of the Buddha - Tibetan Thangka Painting
Buddhism spread eastwards and forever changed China, Korea, and Japan. Buddhism wisely explained the human condition and offered consolation other religions did not give. It also introduced a culture of compassion into societies where survival depended on social status and where poverty was cruelly abundant.
But the new religion did not only impacted the society as such. It also changed the political constellations in these countries. And while other strong religions competed for political influence in Chine or Japan, countries such as Thailand, Tibet, or Burma became Buddhist kingdoms.
The entire south East Asia was changed by Buddhism - its philosophy and aesthetics. A monastic cult…

### healing properties of howlite

Howlite is a calcium boron-silicate hydroxide that usually occurs in sedimentary rock formations. This mineral was named after a Canadian mineralogist Henry How who first discovered it a Nova Scotia gypsum quarry in 1868.
Tumbled white howlite healing crystals
The gem has a rather dull, porcelain-like white or ivory color with pronounced grayish veins that make it look like an albino turquoise. This fact is sometimes exploited by dishonest gem dealers who dye it and sell it as the more expensive turquoise.
Howlite is a rather soft mineral with a hardness 3.5 on the 1-10 Mohs scale. It dissolves in a hydrochloric acid solution.
It forms nodules that can be quite large and look like cauliflowers. Crystals are rare and sometimes form spiky aggregations. They are translucent or transparent, creamy white or light brown.
The largest deposits of howlite were found in Canada, mostly in Nova Scotia, but this mineral is also mined in the USA, especially in California, and in South Africa.
H…

### how to make a gem elixir

Gems and crystals fascinated people since the beginnings of humanity. Their beauty was only one aspect that attracted attention of our ancestors. Most importantly, they discovered their magical powers and learned how to apply their healing properties. Over the ages gems became a vital element of the holistic approach to health.

Gems were used for healing in many cultures. We find them in the Stone Age cultures, in ancient Egypt, China and India. We read about them in Old Testament and in works of Aristotle and find prescriptions in Middle Ages.
The modern crystal therapy is based mostly on the work of the Medieval abbess Hildegard of Bingen who systematized crystals and their properties and incorporated gems into a holistic health concept. She used gems and crystals both, externally and internally: the healing stones were either placed on the body or used in preparation of elixirs that were to be ingested by the patients.

To make a gem elixir simply place cleansed gems - raw or t…

### healing properties of carnelian

Carnelian, also known as cornelian, is a translucent, micro-crystalline chalcedony quartz. It is closely related to sard and sardonite which only slightly differ in color and hardness. Its color ranges from orange and pale red to dark brown and comes from iron oxide (hematite) colloidally dispersed in the trigonal crystalline structure.

Carnelian is a rather prevalent mineral. It occurs in the cavities of many rock formations, but most often it develops silica-rich rocks that solidified at low temperatures but it is also found in volcanic rocks. Carnelian typically forms nodules and cone-shaped masses. Considerable amounts of Carnelian have been found in India, with some of the oldest known deposits in Bengal. Carnelian is also mined in Brazil, Uruguay, USA (mostly in Texas, Colorado, and North Carolina), Botswana, Madagascar, and South Africa.

In the Middle Ages carnelian was called carneolus. This name derived from the Latin word carneus which meant fleshy, made of flesh. The Frenc…

### healing properties of smoky quartz

Smoky quartz is a macro-crystalline variety of quartz. Like other quartz crystals smoky quartz is a silicon dioxide mineral. It usually forms transparent hexagonal, rhombohedral crystals. Macroscopic crystals commonly occur as horizontally striated hexagonal prisms terminated by a combination of positive and negative rhombohedrons forming six sided pyramids.

The name smoky quartz derives from the smoky color that ranges from grayish-brown to dark brown and even black. The smoky color results from natural exposure to radiation. It forms from free silicon that was released from silicon dioxide during the formation of crystals. Smoky quartz is a rather prevalent mineral that is mostly mined in Colorado, USA, in Brazil, Australia, Madagascar, Switzerland, and Scotland where it is considered to be a national gemstone.
Since ancient times smoky quartz was used in many cultures because it was rather easy to cut it to gems and ornaments. This beautiful crystal was considered s…

### healing properties of apophyllite

Apophyllite is a potassium-calcium fluoride-silicate mineral from the family of phyllosilicates. It is structurally related to the zeolite family of minerals and commonly found with zeolites in basalt, granite, and gneiss formations. Like the zeolites, apophyllite has high water content and therefore, good energy conducting properties.

Apophyllite forms cubic or pyramidal crystals that can either be transparent or opaque. The color ranges from white, green, yellow to peach. There are also colorless forms. The name apophyllite is derived from the Greek word apophylliso which means "it flakes off". When heated, apophyllite loses its water and begins to flake.
Apophyllite is a fairly prevalent mineral. It can be found in abundance near Trentino in Italy, near Belfast in Northern Ireland, on Faroe Islands, near Kimberley in South Africa, and in Guananjuato in Mexico. Considerable amounts are also found in the Harz Mountains in Germany, on Mont St. Hillaire in Canada,…

### healing properties of aquamarine

Aquamarine is a variety of beryl. It is a relatively common mineral that mostly occurs in pegmatite rocks and is often found together with the ordinary beryl. The biggest deposits were found in Brazil, Colombia, United States, Kenya, Madagascar, Malawi, Tanzania, Zambia, Russia, India and Pakistan.
Aquamarine with Muscovite
Aquamarine forms pyramidal crystals that can be quite large. Its color ranges from pale blue and transparent turquoise to bluish-green and depends on the concentration of the iron particles within the hexagonal crystalline structure of beryl. Heat is often applied to improve the color of aquamarine crystals. The bluish-greenish hue is responsible for the stone's name which comes from the Latin "aqua marina" or sea water.
The stone was well known and valued in Antiquity. It was regarded as a symbol of peace and tranquility. Aquamarine jewelry was highly prized not only for its beauty, but also for its protective value especially for sailors and those …

### healing properties of phenacite

Phenacite, also known as phenakite, is a rare beryllium silicate mineral that has been traditionally used as a gemstone. Phenacite has been mined together with emerald and chrysoberyl from the mines near Yekaterinburg in the Urals region of Russia where it was usually found in form of large crystals embedded in mica formations. Phenacite is also found in granite formations of Urals Mountains, Russia and Pikes Peak region of Colorado, USA. Considerable amounts of phenacite are also found in Madagascar, Myanmar, Norway, and Zimbabwe. Probably the most beautiful phenacite comes from the Minas Gerais near San Miguel de Piricicaba, Brazil. The stones excavated from these mines are famous for their rare beauty and exceptional clarity.

Phenacite occurs as very well formed free trigonal (rhombohedral) crystals, large prisms, or relatively small prismatic wands. It may also form a small clusters. Phenacite is either transparent or milky and comes in different colors. Very often it i…