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> When scientists are playing Issue: 2011-1 Section: Math



When scientists are playing


Ana Ilinca FOTA


Even if it seems strange to imagine adults playing, at least honorable scientists, as long as playing refers to a range of voluntary, intrinsically motivated activities that are normally associated with pleasure and enjoyment and it has been proved as being an imperative for all higher-functioning of animals, then… adults are allowed to play.

What happens when scientists are playing …this is already a statistical story!

For example, Johannes Kepler (1571-1601), already famous for his researches at the time – being the imperial astronomer of Rudolph II (1552-1612) - wrote an essay On the Six-Cornered Snowflake.

Playing with words (in Latin – the language of the essay - nix meaning snowflake, but in German – the native language of the author- nix meaning nothing). Even if circumstantial and not scientific reasons made him at first to write the essay, the scientist overcomes the common issues and finally he concluded that a snowflake might be a perfect Christmas gift since it comes down from heaven and looks like a star. From this point on the essay talks about geometrical figures, being the very first known published work that describes and analyses the structure of the ice crystals, even on lyrics.

For him the beautiful six-cornered snowflake was just another marvelous example of the natural harmony concept. However, fascinated by harmony and relating the concept of congruence to diverse categories of the physics (three dimensional geometry, relationships among different species of magnitude, principles of consonance in music, organization of the Solar System) Kepler considered the Harmonices Mundi (The Harmony of the World, 1619) his most important work.

But water and especially its crystals continued to puzzle and fascinate scientist over centuries.

We’ve been taught from the earliest ages that water is the basic substance for life on Earth, and we never doubt it but step-by-step we discovered even more.

Water covers 70,9% from the Earth’s surface, as well it represents about 70% of the human body composition and between 2% and 98% of the other living forms (plants and animals). It is widely present, supports life as we know it and its properties seem to be largely known However, what makes it unique and indispensable for Live on the Earth? Dihydrogen monoxide (H2O), the tasteless, odorless and, up to an extent, colorless substance commonly named water, unlike other hydrides (which are on gas phase at normal temperature, e.g. hydrogen sulfide) remains liquid on normal conditions. Even more, its solid phase (ice) is floating onto the liquid one being less dense than the liquid one (fig. 2). Actually, water is the only known substance on Earth where the maximum density of mass does not arise when it becomes solidified but at around 4 °Celsius, in liquid phase; thereafter, freezing it expands rapidly gaining almost 9% by volume due to the spatial arrangement and the electrochemical properties of the molecules (fig. 3).

The very simple atomic structure of water causes its molecule to have electrochemical unique properties; the hydrogen side of the molecule has a slight positive charge while the other side has a negative one.

This makes water a powerful solvent able to solve-minerals from soil and next its very high surface tension, responsible for capillary action, helps feeding plants making life possible on Earth. Water has many other amazing properties, like its complete natural-cycle taking only nine days- the most perfect example of what renewable must mean in the very essence of the concept; its vapor phase movement through atmosphere and its liquid / solid phases transformation determine the climate on Earth. Consequently, water is a challenging substance that continues to puzzle scientists.

Few centuries later, an another scientist, the well known Romanian academician and engineer, aviation pioneer and the inventor of the modern jet aircraft Henri Coanda (1886-1972) was fascinated by harmony, symmetry and fluids’ flow. His aerodynamic effect now known as the Coanda Effect (patented in France, 1934) would not be discovered if the author wouldn’t be an advised observer and a good analyst on fluid mechanics’ phenomena (fig. 5, 6).

Moreover, between the 1910’s fuel leaks incident that jeopardized his Coanda-1910 airplane model at the second International Aeronautic Salon in Paris and the year of the Aerodynamic Effect patentee (1934) Coanda discovered (as he mentioned in one of his interviews) the amazing properties of water, on its different phases, and he become fascinated (for the rest of his life) on its crystallization (fig. 7a, b). Actually the aerodynamic Coanda effect, as it can be observed on water flow, vortex and other powerful dynamic models were studied by Coanda firstly on more viscous fluid (water) and then adapted to the gasses dynamics. Those modeling steps made seventy years ago making easier the computer modeling of nowadays (fig. 5a, 6b). Even if he didn’t published any work based on his water and snow studies, he invented a machine to make artificial snow, firstly for study reasons, but later on this became the first source of artificial snow produced for the ski slopes (France, 1930’s). In 1963 Coanda presented a test model of a shrouded Coanda Effect internal nozzle he designed for underwater propulsion using steam as the primary fluid. However, his publicly known scientific activity has been focused mainly on aerodynamic area, but one life-long passion remained the study of ice, encouraging promising young scientists on a think-tank at NASA (1964) to solve the mysteries of water and ice.

Meanwhile, at the middle of the 20th century when people didn’t shared their ideas through World Wide Web in no time as we do now, another scientist, in Japan, dedicated his entire life to the study of ice crystals. The famous Japanese physicist and scientist of snow and ice Nakaya Ukichiro (1900-1962) (fig. 8a) left a clearly settled classification of snow crystals (fig. 8b), using for his observation the best existing characterization equipments of his time and designing an equipment for making artificial snow on lab conditions (fig. 8c). Interesting, hundreds years after Kepler’s essay to Snowflake another scientist have to wrote …snow crystals may be called letters sent from heaven (Ukichiro Nakaya, Snow Crystals, 1939). Worshiping his research on natural and artificial (fig. 8b) snowflakes, a Museum of Snow and Ice – a hexagonal building remembering the six cornered shape of snowflakes- has been raised at Ishikawa, Japan. And the snowflake story continued; based on Ukichiro’s published studies few years later a complete diagram showing the dependence: supersaturation, temperature and snowflake form was published (fig. 8d). Then suddenly, especially in the last two decades, the scientific research tools improved essentially and the characterization and all previous observations could be reassessed by electronic microscopy techniques (fig. 9). This time research centers of famous universities dedicate special programs to snow and snowflake crystallization studies, and especially on solving the challenging issues on modeling the crystallization process. So, presently worldwide mathematicians are using models to simulate snowflake growth knowing that a snowflake is a single crystal of ice usually having a hexagonal prism form (fig. 9) but temperature, humidity (supersaturation), impurities, pressure variations, and other variables can influence the snowflake’s shape.

How? There are networked multidisciplinary scientists working at this. Some of them are making high accuracy pictures of the real snowflakes in their environment using specially designed equipments and software (fig. 10a); others are developing computer programs aiming to mimic the growth principles of real snowflakes.

After more than 400 years of wonderings and searches, mathematical models running on powerful computers can mime how snow crystals would grow (fig. 10 b-d); about the shape…it remains a mystery, yet largely unpredictable but on the frontage of crystal growing simulation in all biggest research centers. That makes us really doubtful when scientists are playing …



  • Garvey, C. (1990). Play. Cambridge, MA: Harvard University Press
  • Pidwirny, M. (2006). "Physical Properties of Water". Fundamentals of Physical Geography, 2nd Edition
  • Nakaya, Ukichiro (1954). Snow Crystals: Natural and Artificial. Harvard University Press. ISBN 978-0674811515.