ticks to tocks

how does a tick turn into a tock
forty-three thousand two hundred times a day?
does it know how to walk, talk, learn, laugh, and leap,
or does it only know not to stay?

is it the gears within, grinding with grit
or the pendulum’s beautiful sway?
is it the springs that are sprung, abruptly undone
that kick the seconds away?

is time just a thought, on the surface of naught
and the clock just a rhythmic display?
a heartless dimension, one of invention
no care for the world at bay

or is every tick that makes it to tock
a reminder that life if okay?

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How Fast (Or Slow) Is The Speed Of Light?

A Little Background

The first recorded discussion regarding the speed of light was in and around 300 B.C. where Aristotle quotes Empedocles as theorizing that the light from the sun must take some time to reach the Earth. Almost two millennia later during the Scientific Revolution (circa 1620 A.D.), Descartes theorized that light was instantaneous. At about the same time, Galileo gave a more general thought that light was much faster than sound but not instantaneous, offering up some ideas as to how it might be tested using lanterns and telescopes. At what point would these theories actually be tested and how?

About half a century after Descartes and Galileo, the Danish astronomer Ole Römer began measuring the actual speed of light through observation of Io, one of Jupiter’s moons. He recognized that as the Earth and Jupiter moved in their orbits, the distance between them varied. The light from Io (reflected sunlight) took time to reach the earth, and took the longest time when the earth was furthest away.  When the Earth was furthest from Jupiter, there was an extra distance for light to travel.  The observed eclipses were furthest behind the predicted times when the earth was furthest from Jupiter.  By measuring the difference in time and using a little math, the speed of light could essentially be calculated.

From that point forward, numerous scientists tackled this quest through a diverse set of accompanying theories and experiments. The speed of light would be more accurately determined, leading to wide applications in optics, astronomy, and physics. For example, in the early 1900’s, the speed of light became a foundational component of Einstein’s theories (general and special) of relativity, proven to relate energy to mass (E=m*c^2 where c = speed of light). As a result of these applications, the calculation of the speed of light was a major platform for new scientific discovery and enlightenment.

So How Fast Is It?

Well, the measured speed of light in a vacuum is exactly 299,792,458 meters per second, often approximated as 300,000 kilometers per second (3.0 * 10^8 m/s or 3.0 * 10^5 m/s) or 186,000 miles per second. Outside of a vacuum where there might be atoms and molecules that act as impeding forces, the speed of light slows down based on the refractive index of the material. For a given substance with refractive index (n), the actual speed of light (v) is given by v=c/n where c is the constant speed of light in a vacuum. Of note:

v(air) = 299,704,764 m/s (n=1.0002926 at standard room temperature)
v(water) = 224,900,568 m/s (n=1.3330)
v(salt) = 194,166,100 m/s (n=1.544)
v(diamond) = 123,932,392 m/s (n=2.419)

Let’s put the speed of light, in air, in a bit of context…

The circumference of the Earth is about 40,000 km on average. That means that light could travel around the Earth 7.5 times in a second.

The distance between the Earth and its moon is about 380,000 km on average. It takes light about 1.27 seconds to travel from one to another. Click here for a demonstration.

On the size of our solar system, it takes light from the sun about 8 seconds to reach Earth, 43 minutes to reach Jupiter, and nearly 7 hours to pass the orbit of Pluto.

On the size of our galactic realm, the Milky Way is a spiral galaxy. Our solar system is located on what is called Orion’s arm, about 25,000 light years from the center of the Milky Way’s center. One light year is the distance light travels in one Earth year. In more earthly terms, that’s about (3*10^5 km/s)*(60 s/min)*(60 min/hr)*(24 hrs/day)*(365 days/yr) = 9,460,800,000,000 kilometers. And I thought a marathon was far.

Beyond our Milky Way galaxy and looking at our Local Group of galaxies, it extends about 4 million light years across. That means for light to run from a galaxy one side of our Local Group to a galaxy on the other side of our Local Group, it takes 4 million years. Yikes.

And our Local Group of galaxies is part of a larger “supercluster” that is 150 million light years across. The dinosaurs roamed Earth from 230 million to 65 million years ago. In other words, light from the Ursa Major and Virgo galactic clusters still hasn’t reached us if it was emitted during the extinction of dinosaurs. Makes light seem pretty slow now, no?

Whether quick relative to earthly distances or slow through vast cosmic voids, even light has meaning. It provides perspective, foundation, discovery, and well, light.

For more on the speed of light and the depths of the universe and time, I highly recommend Bill Bryson’s A Short History of Nearly Everything (it’s my favorite book).

Boundaries Of The Human Condition

“That ideas should freely spread from one to another over the globe, for the moral and mutual instruction of man, and improvement of his condition, seems to have been peculiarly and benevolently designed by nature, when she made them, like fire, expansible over all space, without lessening their density at any point, and like the air in which we breathe, move, and have our physical being, incapable of confinement or exclusive appropriation.” – Thomas Jefferson

There exist many concepts and rules by which we are bound, some of which we may be aware and some of which we may not be aware. Those concepts and rules of which we are aware exist throughout nature and space because we can observe them and learn them, manipulate them and control them, and hear them and speak them. Those concepts and rules of which we are not aware exist because we cannot observe them and learn them, manipulate them and control them, and hear them and speak them. In a sense, we are bounded by that which we can know and cannot know – although those boundaries can and will change throughout the course of history.

It’s interesting to think about our intellectual boundaries, limits, and intersections because they can be sliced and diced a thousand and one different ways. To a chef, his or her capacity may be bound by a colander, letting some things in and others out, clogged and dirty at times and crystal clear at others. To a biologist or chemist, he or she may see it as some semi-permeable membrane that expands and contracts, filters substances based on the needs of the whole system. And to an astronomer, the boundaries may be the vast unknown of our universe: with new discovery always comes more knowns coupled with more unknowns.

Regardless of the profession, it’s valuable to think about. For me, I’ll gladly wear the shoes of a different scientist each waking day but to start, here are a couple different categorizations of our intellectual boundaries, just to jot some thought.

Spatial Dimensionality

Think of our intellectual capacity as bounded by one big room. This room can grow as it’s supported by more material, can shrink with the absence of structural connections, and can lose energy with a loss of insulation, cracks in the windows, etc. It can become more complex or simple in a hour’s time with the addition or removal of new features and can take on a new look and persona with the manipulation of a few simple characteristics such as paint and fixtures. You get the point.

Walls – The walls are the support and protection, and are the primary means by which we are bound. The walls are our rules of lateral movement, being, and knowing. In a room of infinitesimal walls, we’ll find just as many corners (getting us ever close to the perfect circle) but we’ll still be limited by a surrounding perimeters. In our room, the walls are our physical concepts, our school subjects, our theorems and laws, our rules of society.

Floors – The floors are our foundation. Without the floor we would not be able to maintain our position and as a result, move from one position to another. The floors are our foundation for thought – our family, our circumstance, our physicality – our reference point.

Ceilings – The ceiling is our limit. The ceiling provides cover and security, shape and reflection, and a foundation for belief and new thought. The ceilings are our hypotheses and conjectures, our gateway to the unknown as much as it they’re the gateway for belief and clarity of vision.

Corners – The corners are the intersections of life, the crossroads of knowledge and new thought. Every corner is formed by the other structures mentioned above. The corners are the relationships, the interdisciplinary nature of life, the idea that everything is connected.

Existential Dimensionality

Now think a bit differently. Think that our intellectual capacity is bounded by core concepts which, when intersected, form feelings, thoughts, beliefs, and understanding. The core concepts are the things we should study – the basics of existence from which we should gain our foundations. I spoke about studying people earlier, with an overview of Archimedes. For the places, I’ll talk about some of my 2010 visits in the near future. And for time, we’ll it’s the scale by which we can make sense of history, and the perception and reasoning that comes with it. The triangulation of these three things gives an enclosure of feelings, thoughts, and beliefs that form the boundaries of our intellectual capacity.

People – We are who we are as much as we are who we’re with (and who used to be with us). To feel, learn, and think, we must understand how other people feel, learn, and think (or felt, learned, and thought). This is core to society, law, science, religion, and everything else.

Places – We are who we are in the place that we are. If I were in a different place right now, my actions, feelings, thoughts, and beliefs may be different as a result. Place is a part of circumstance which most certainly contributes to our thoughts and beliefs.

Time – We are who we are because of the historical context in which we live. Time forms this context and provides structure to the way we think, how we can act, and as a result, what we might think and believe.

Feelings, Thoughts, & Beliefs – Our coordinates at any one time (say, x=people, y=place, z=time) describe who we are. The result of who we are is an output of feelings, thoughts, and beliefs. These form the boundaries, limits, and intersections of our intellectual capacity. Change coordinates, and we’ll find new outputs. And the most important thing to note: as with mathematical coordinate systems, there’s no limit to our coordinate system space, only to a local solid surrounding a group of coordinates. Limits may exist on my axes, by not on the coordinate system as a whole.

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