Koch Snowflake

Yesterday work found me on a luxury yacht, a 60th wedding anniversary celebration with finicky moving parts. As chefs began plating passed canapes I voiced dissatisfaction with presentation – no symmetry please! Later that night one of the chefs, a close friend and co-worker of nine years messaged – in all our years working together why haven’t you corrected my symmetrical arrangements? Adding, “Google informs me  “Symmetry in everyday language refers to a sense of harmonious and beautiful proportion and balance”. He asked “what would you call your preference? Randomness, disorder or perhaps asymmetry “. I replied, “Ask any staff member what makes me crazy, I guarantee one of two answers – symmetry or bartenders who put caps on empty wine bottles.” My preference? Asymmetry of course!

Why asymmetry? What compels me to hammer notions of symmetry out of new staff? Why do long-time staff members laugh out load when they hear me train new staff, “pay attention” they chime, “she hates symmetry, no bookends, twos or fours, only threes and fives”. Cheekier staff punctuate with “relax, as long as it’s random she’ll be happy”.

Random? Asymmetry isn’t random, it’s pleasing and calculated to my eye! Without warning a fractal bomb went off – wait a minute, fractal symmetry is absolute perfection!

Ponders scurried from Mandelbrot Sets to Koch Snowflakes.  From https://fractalfoundation.org/resources/what-are-fractals/ “A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. Abstract fractals – such as the Mandelbrot Set – can be generated by a computer calculating a simple equation over and over.”

In 1904 Swedish mathematician Helge von Koch published a paper titled “On a Continuous Curve Without Tangents, Constructible from Elementary Geometry” – translation, one of the first published fractal theories. Koch Snowflake is an elaboration of the Koch Curve. Be it curve or snowflake, fractal mathematics are the same – whenever you see a straight line divide it in thirds, build a equilateral triangle on the middle third, erase the base of the triangle so it looks like the shape to the right.

Animation of the first seven Koch Snowflake iterations –

Koch Snowflake

Shortly after his first query, my friend reminded me of mutual affinity for Mandelbrot sets (example below). So why asymmetry, he pressed. Why, indeed?


Oh man, I replied! It’s too late for this ponder! Obviously fractal symmetry warms my heart, but until the day chefs definitively represent fractal perfection with smoked beet tartare on a passing platter – asymmetry remains an art form, symmetry makes me cringe. Go figure.

Carl Sagan Explains The 4th Dimension

A few minutes ago YouTube displayed video of Carl Sagan explaining the 4th dimension on my Home page – well played YouTube! Smitten of late by Neil deGrasse Tyson, pondering the enormity of Sagan’s influence, accomplishments and reason seemed long overdue.

Time magazine called Sagan “America’s most effective salesman of science”. Faint irritation nibbled at the realization I didn’t know how to proceed. Biographical bullet points wouldn’t do, I wanted to impart subtleties of wonder sparked by his influence. Thoughts meandered to his corduroy jacket, an unfortunate fixation that wasn’t making things easier. Then it came to me – Carl Sagan’s reach can be introduced, acknowledged or discovered dependent on individual experience. Rather than fret over conveying my appreciation to a generation untouched by his perceptible impact, it was enough to appreciate contributions by posting his explanation of the 4th dimension.


Oh, grow up out of your preschool dimensions!

Tonight’s work day evolved into several hurry up and wait hours. A low key wedding demanding nothing more than post coffee and dessert kitchen talk. A co-workers expressed interest in the 4th dimension. Oh man I replied, send you a few outstanding links when I get home. I’d forgotten how great geneticfractals perspective was –

Gravitational Time Dilation

Excessive contemplation works in mysterious ways, I didn’t wake up pondering gravitational time dilation. Placing blame squarely on GPS strikes me as a reasonable explanation. I brought it on myself – putting a monotone tyrant in charge before first coffee rubbed sleep from my eyes, obviously explains an inexplicable need to understand Einstein’s theory of relativity. With each directive – turn left, right, merge – absolute faith in GPS freed my mind to concentrate on time and space.

We think of GPS as an absolute tool, one linking position of our device with that of some imagined all seeing eye. Few of us realize GPS constantly recalculates and adjusts readings based on Einstein’s theory of special relativity. If left unchecked, navigational errors of 10 km per day would quickly topple getting from point A to B.

Einstein’s theory of relativity describes the effect of gravity on space and time. Time is relative to mass and proximity of gravitational pull – speeding up as it moves further away. Time passes at different rates according to gravitational potential. Space-time depends on proximity to forces of gravity.

GPS satellites orbit 20,000 Km above, with gravitational forces four times weaker than Earth. Science proves Einstein knew what he was talking about – satellite clocks tick 38 microseconds faster a day than clocks on our planet. I urge you to read the link below. It explains gravitational time dilution – I’m still digesting my first dip in the relativity pond.





Explain Yourself Hadron

Science wires reverberate with news of the Large Hadron Collider (LHC) once again accelerating particles following a 2 year hiatus. Catching wind of LHC successfully out of the starting blocks this past Sunday, my initial reaction was “holy crap, that’s fantastic”. Officially LHC shut down in February 2013 for “upgrades” and maintenance in preparation for this week’s curtain – particle collisions at almost double the previous velocity.

In 2013, the Nobel prize in Physics went to Francois Englert and Peter W. Higgs for theories developed in 1964 on how particles acquire mass.

The awarded theory is a central part of the Standard Model of particle physics that describes how the world is constructed. According to the Standard Model, everything, from flowers and people to stars and planets, consists of just a few building blocks: matter particles. These particles are governed by forces mediated by force particles that make sure everything works as it should.

“The entire Standard Model also rests on the existence of a special kind of particle: the Higgs particle. This particle originates from an invisible field that fills up all space. Even when the universe seems empty this field is there. Without it, we would not exist, because it is from contact with the field that particles acquire mass. The theory proposed by Englert and Higgs describes this process.

On 4 July 2012, at the CERN laboratory for particle physics, the theory was confirmed by the discovery of a Higgs particle. CERN’s particle collider, LHC (Large Hadron Collider), is probably the largest and the most complex machine ever constructed by humans. Two research groups of some 3,000 scientists each, ATLAS and CMS, managed to extract the Higgs particle from billions of particle collisions in the LHC.

Even though it is a great achievement to have found the Higgs particle — the missing piece in the Standard Model puzzle — the Standard Model is not the final piece in the cosmic puzzle. One of the reasons for this is that the Standard Model treats certain particles, neutrinos, as being virtually massless, whereas recent studies show that they actually do have mass. Another reason is that the model only describes visible matter, which only accounts for one fifth of all matter in the cosmos. To find the mysterious dark matter is one of the objectives as scientists continue the chase of unknown particles at CERN.”


Back to my “holy crap, fantastic” – recognizing magnitude, does little to solidify that event in accessible terms. I can “holy crap” all week long, “fantastic” would be wrapping a middle aged head around theoretical physics. Toss me a crumb Hadron, you have my undivided attention. Out there somewhere is a merciful person or website  capable of patient baby steps from the Standard Model to ramifications of your greatness.

Towel and Apple Clarify Big Bang

By now many people have caught wind of this weeks announcement, scientific confirmation of the inflationary universe theory. Images of “primordial gravitational waves” captured by the BICEP2 project – an experiment headed by Professor Andrei Dmitriyevich Linde,  give unprecedented proof our universe is expanding.

Talk of expanding universe theory sends most people running from the room – I get it, it’s hard to understand. Never fear, I’m about to make it clear. Spend two minutes watching this video – without question the best two minute lesson around.

Bonus points awarded for anyone who links below to another video of Professor Linde being surprised by a colleague with the news.


The Conspiracy Conspiracy

I don’t believe we are alone in the universe; it isn’t reasonable to think in all those millions of galaxies some form of life doesn’t exist. The belief our world is only 6000 years old strikes me as pure lunacy; a sentient being did not create the world in less than a week. The 140 million mile wide black hole at the centre of the milky way galaxy is not the stairway to heaven. Cuttlefish can instantly change; not only the colour, but texture of their skin because evolution is a weird and wonderful thing. Not for one second do I think our historical timeline is accurate; history , civilization lost, whatever you want to call it, existed thousands of years before textbook history class. Governments keep us on a “need to know” basis, and money makes the world go round.

This makes me a conspiracy theorist; a person dismissed as “out there”, someone who dines on ancient aliens and buys into any hair brained argument that comes along. It isn’t about religion, science or politics; the tables have turned, I’ve been branded – open my mouth about Gobekli Tepe. Puma Punku, even solar flares and eyes start to roll. The other night I caught about 5 minutes of a TV show called Conspiracy Theory with Jessie Ventura; the subject was time travel. Jessie and his “team” were getting to the bottom of secret time travel conducted by the U.S. government, a whistle-blower claimed time travellers visited American presidents before they were elected, informing them of their destiny. I’m not able to say the how or why because something dawned on me while scrambling to change channels.

The conspiracy conspiracy seemed the only plausible explanation. Take ex pro wrestler, turned former Governor of Minnesota, Jessie Ventura; throw in Oliver Stone’s son as one of his “investigators”, turn them loose on scripted nonsense, pretty soon the mere mention of something unexplained smacks of crazy. Pure and evil genius.

Pole Reversal

Historical and scientific records indicate many earth shattering events are long overdue. The “big one”, referring to a mega earthquake in the pacific north west, the Yellowstone super volcano, and apparently – a magnetic pole reversal.

I always believed theories of pole reversal lived only on the pages of books. Discovering this event is not only probable, but has happened in our history on more than one occasion, gave birth to this ponder.


Andrew Biggin from the University of the Netherlands in Utrecht, analyzed rock to determine how they were magnetized at formation. This allowed him to pin point the location of the magnetic pole at the time. His research showed a reversal every 400,00 years or so; the last one taking place about 800,000 years ago. He suggests that a pattern of  weakening in the earth’s magnetic field takes place for around 2000 years prior to the complete reversal. Archaeological evidence indicates our magnetic field was considerably stronger in Roman times.

Pole reversal doesn’t happen overnight; overdue, in earth terms could be hundreds, thousands, or millions of years. Just one more reason to ponder our time on earth. One more reason to embrace each day, not sweating the little stuff.

Dark Matter

The universe is made of matter, normal matter is the matter we understand. Normal matter makes up only around 5% of the universe. The rest – about 70% is dark energy, and 25% dark matter.  We have no idea how dark energy or matter work, we only know it’s there. To understand them we may have to throw Einstein’s theory of relativity out the window, as his theory on gravity holding the universe together doesn’t seem to apply to 95% of our universe.

.Albert Einstein