Friday, May 29, 2015

The Golden Ratio - A Hidden Symmetry

"Phi" the Golden Ratio, also known as the divine proportion has fascinated mathematicians for over 2,400 years. As an artist with a BA in graphic design and a minor in art history I can confirm artists do study this ratio in great detail and it does exist in both art and architecture. It's not always obvious in a classic painting until your professor points it out, but once you see it you know its there. In some paintings it's a hidden triangle with points of light, but its never obvious. This magic "exact" number or Phi, is observed when taking ratios of distances across the board in the context of science, nature, architecture, sculpture, painting and music. In nature, zoologists recognize the ratio -  1.618 as the logarithmic equation to a spiral, the curvature of an elephant tusk or the shape of a Kudo's horn. In meteorology its recognized in the spiral of a hurricane, and in the cosmos its seen in the spiral of a galaxy. It seems this cosmic "constant" (T) is found everywhere as an infinite constant. To summarize: if "a + b" is the whole line, and "a" is a larger segment and "b" is a smaller segment, then: (a+b)/a = a/b + Phi. The shortened numerical value of the Golden ratio mathematical equation is actually 1.61803399.

Despite many people's assumptions to the contrary, the fine arts are full of math. A battle between elegant symmetry or chaos, a painting can sometimes be all about math and the Golden ratio. As the Golden section is found in designs and the beauty of nature it can also be used to achieve beauty and balance in the design of a painting. For instance, as an artist you have to know the rule of thirds. Nothing is more boring than a painting split in half. That's why when you look at the landscape you'll see often see a two thirds / one third composition. A succesful landscape will have the sky for two thirds of the painting, and the land at the bottom third or vice versa. One thing I can say about the arts is, at least we know how to apply the Golden ratio. We may not know exactly what it means but there's no doubt we use it over and over to get a balanced composition, and we have been for hundreds of years.  On the other hand, the very science that lead us into our own useful application seems unsure of the evidence. Scientific research of the Golden ratio seems to be considered more of an intellectual curiosity than a technical insight, but new evidence is illustrating how this mathematical theory actually exists.

For instance in 2009 - a scientist named Calleman reported the Golden Ratio is involved in the universal Bohr radius fromula, when a single electron orbits hydrogen's atoms nucleus and its smallest possible orbit with lowest energy is the most likely position of  a number matching the golden mean. A year later in 2010 an international team of researchers observed a nanoscale symmetry hidden in solid state matter that showed the same attributes as the Golden ratio. To reveal the hidden quantum symmetry they worked with a magnetic material cobalt niobate in chains only one atom wide and observed that these atoms acted much like a guitar strings that resonated in a series of notes, with frequencies in the ratio of 1.618. Such discoveries are no coincidence and in this case, the researchers didn't believe it was either. Dr. Caldea, the lead researcher said it reflected a beautiful property of the quantum system - a hidden symmetry. Actually quite a special one called E8 by mathematicians, and this is its first observation in a material.

Strangely enough, for the last 20 years, our very own DNA coding has also revealed models of fractal integer patterns like Fibonacci or Lucas numbers which are deeply connected to the Golden ratio as well. In 2010 a exhaustive study proved that  codon populations in single stranded Whole Human Genome DNA Are fractal and fine tuned by the Golden ratio 1.1618. The paper was published in Disciplinary Science 2010 by Jean-Claude Perez.

Maybe the time has come to recognize that relativity and quantum theories can be integrated and linked numerically to the value of a mathematical constant. This ratio of hidden symmetries seems as if it's trying to tell us something important about connections. There seems to be a lot of skepticism about the idea but evidence is out there and to be honest I think some people lack imagination. Imagination is a powerful tool used in science and art, and mathematics has played a key role in physics and understanding the laws of nature and the universe. Whether art, space-time or biology, the Golden ratio is a great mystery I hope we can use to the best of our knowledge someday with this very unique number.


Monday, May 18, 2015

Predicting The Future

The next two hundred years is a future difficult to predict, but as I wrote the Phobos series I found myself thinking about timelines. Inside these timelines I looked carefully at what has changed in the last two hundred years, but I also reflected on a few things that haven't changed in the last 200 years or 2000 years for that matter.

Part of the challenge of science fiction is envisioning the future as a whole, good or bad but also imagining the details and everyday life of someone. Would wine still be around? What's in our medicine cabinets and in our homes? Do we smoke cigarettes? Are we married? Do we work? Do we have families? What is on our plate in the future, and on our tables?

Well, certainly I think wine will be on the table, and I tend to believe a family will be sitting around it too. Marriage might go out of style and back in, but I don't see a future where men and women ever lose the desire for love and commitment, or the capacity for jealously and hatred.  Of course, no one can predict the future but there's certainly some things that will never change.

Lets not forget among these natural chords of humanity, that technology can only do so much in the face of disaster, and we are often at the mercy of nature, so be prepared.  Things could get shaky if apocalyptic weather conditions crop up and so will food supplies. Although we have the ability to adapt with genetic crops and super vitamins, nothing can stop over population. Government food rations, famine and hardship mixed in with medical advances, cars that drive us, homes that talk to us, and drones that protect us or spy on us in every manner seems like a possible scenario. Maybe gas becomes kilowatts, and dollars become credits, but certainly energy becomes the price. As far as smoking, maybe 200 years from now cigarettes are healthy, using nothing more than flavored water vapor that is medically beneficial. Only the "health nuts" will be smoking. I imagine perhaps, that despite many things, medical technology will always take leaps and bounds. Communication will be a fun one too.

The questions is, in the worst case scenario, what would we do? A small colony on Mars could be an answer if things got bad enough. Just how bad would things have to get, well, I'll leave that up to the future about 200 years from now and inside the pages of my story.  Maybe just maybe, there is a small colony...

Wednesday, May 6, 2015

Ice X, An Exotic Discovery


Ice is a mystery, and a fascinating material. For planets closest to the Sun, water ice dominates, but farther into the solar system, other types of ice exist.

Next time you put some ice in a drink, take a sip and let your thoughts reach beyond your glass, because ice is actually a unique and exotic form of water, and its only ONE of several solid states that can exist. Ice exists throughout the solar system, from the planets closest to the Sun, to the far reaches of the mysterious Oort cloud, a vast and diffuse wall of comets. From your freezer to the outer solar system, entire planets are made of the stuff or as partial mixtures of ice and rock combined. Ice occurs as polar caps and permafrost and may persist inside the coldest darkest craters of otherwise rocky bodies. Ice may be ancient, present since the birth of the solar system, or young and pristine; recently condensed from liquid. It may have migrated, molecule by molecule.

The ice we know on earth, is Ice I, but water has more than a dozen solid states, only one of which is familiar to us. There are other exotic solid forms of ice that are not cold - I repeat NOT COLD. This what is known as Ice X.  This 'hot' ice is more dense, thicker and heavier than Earth's cold Ice l. It takes an extreme amount of pressure, but water can become a hot ice, and it does exist. Described as a cubic crystalline form from liquid water, a hot ice can be created under very high pressure, when water turns into solid states denser than both ice and liquid water, just as carbon transforms into diamond under extreme pressures.  

These bizarre ice solids can be found on alien planets, or in science labs, made under extreme pressure where H20 is crushed and its molecules are forced into a crystal solid. This means if you flew over one of these Ice X planets and got a good look, you would see a heavy clear plane of solid water, and you could land on it, but it wouldn't be cold. On another planet, you could sink to the bottom of an ocean and find it far underneath, hitting a floor of solid water. These are worlds of compressed H2O, of Ice X and exotic 'hot ice' states. There are also other lower grades of solid ice like 'Ice VII'. Ice VII is just a little less dense made in labs using pressures above 3 GPa, and by lowering its temperature to room temperature, or by decompressing (D20) ice VI below 95K. The higher the pressure the higher the number they give the Ice, but Ice X or Ice 10 needs about (100K 62 GPa) to be made. 

Scientists think that Ice 7 might make up the ocean floor of Titan, one of Saturns moons, as well as extrasolar planets such as Gliese 436b and GJ 1214. Both of these planets are largely made of water.

Are you still enjoying your drink? Maybe you can get a refill before I continue, but all kidding aside, its pretty interesting to think something we took for granted like ice is actually not everything we thought it could be. If you really want to go back in time you'll also find out ice was originally formed from a solar nebula. Our sun, like other stars formed from a cold interstellar cloud of hydrogen, helium molecules and dust. As this nebula cooled, different elements condensed out into grains or ices, depending on their "condensation" temperature. Rocks and metals were formed and as the nebula continued to cool, carbon grains and ices of water, carbon dioxide, nitrogen, and ammonia condensed out. The line between the areas where rocks and metals condense and where carbon and ice grains begin to condense is known as the "frost line." The exact location of the frost line is still debated, but it is thought to be around 4 AU, between the asteroid belt and the orbit of Jupiter. (Earth is 1 AU from the sun; Jupiter is 5 AU from the sun). 

Well, as you can see one mystery seems to beget another as I uncover debates like the frost line. In any case, Ice X is a new discovery for me, that I thought I would share with you, over an icy drink. So lets make a toast to Ice X and other exotic mysteries. As we join our glasses together I say, let's drink to the future. Lets all focus on new exotic mysteries. Maybe we all can see it one day. Maybe. Anything is possible.