Category Archives: Physics

Everything You Ever Wanted to Know About the Winter Solstice (But not really)

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The Winter Solstice is the longest night of the year. In our calendaring system, it also marks the first night of winter.

But in many ancient European calendars, the solstice marked mid-winter. In Gaelic calendars, for example there were eight major calendar markers – though it’s disputed how greatly each was celebrated.

The eight markers were made up of the two solstices, the two equinoxes, and then four cross-quarter days – the days halfway between the a solstice and an equinox. These markers divided the year into eighths and governed what is now referred to as the Wheel of the Year.

We essentially still have eight year marker days, but they’ve shifted names and meaning.

Groundhog’s Day, for example, is essentially the cross-quarter day between the Winter Solstice and the Spring Equinox. Today, Groundhog’s Day marks the middle of winter – will the groundhog see his shadow? But more traditionally, it – or more properly Imbolc marked the end of winter and the beginning of spring.

I’ve never been quite clear on how the Solstice went from representing the middle of winter to representing the beginning of winter – perhaps it’s just one of those things, like the Great Vowel Shift.

Also, there was an interesting piece yesterday claiming that this year’s solstice was, in fact, the longest night EVER. Pointing to the continual slowing of the earth’s rotation, the article estimated that every year’s solstice was negligibly longer than the last.

Of course, that could only make me think of Office Space’s Peter Gibbons reflecting that “every single day of my life has been worse than the day before it. So that means that every single day that you see me, that’s on the worst day of my life.”

But, it turns out the original article is not quiet true. They quickly posted a correction, clarifying that while the earth’s rotation is trending towards slowing down, there’s actually quite a bit of year-to-year variation.

And by “quite a bit,” of course, I actually mean changes so miniscule that nobody without a properly calibrated device of some sort would ever know the difference.

In this graphic you can see the average length of a day charted over time. As you can see – maybe – “the longest night in Earth’s history likely occurred in 1912.”

So that was the longest night ever.

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Perfect Circles

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In many cultures around the world, circles have been used as images of harmony, completion, perfection.

I have a vague recollection of a teacher once telling my that this is because circles are so sweetly symmetrical, though I honestly don’t have the expertise to tell you why the circle is so revered.

Perhaps, though, what I find most beautiful about circles can be seen in a force-diagram.

That is to say, what I find beautiful is the answer to the question, why does something travel in a circle?

Circular motion, you see, is the result of two perpendicular forces. One force, inertia, pushes an object in motion to continue in a straight line. Another force, say, gravity or the tension on a string, pulls the object inwards.

One force points towards the center of the circle, the other points tangential to the circle. And it is the conflict and synergy between these perpendicular forces which causes the circular motion to form.

It’s important to note these forces aren’t opposing. An object affected by a force pointing in one direction and an equal force pointing in the opposite direction would go nowhere. It would appear static despite the two very real forces pushing on it.

But circles form from perpendicular forces. At each moment, the object moves a little bit this way and a little bit that way, at the whim of two forces which, perhaps, seem to have little in common at all.

But the object in question traces out a beautiful, perfect arc.

Symmetry from different forces.

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A World with no Friction

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In physics, it is common to tackle complex problems by starting with a simplification of the scenario.

Want to understand how an object move along a surface? Start in a world with no friction. Assume a standard downward force, g, and understand the simplest version of what is going to occur.

Once you have a simple formula for the simple situation, then you can add friction and other real-world complications. Little by little you can expand your simple model into a complex model, slowly but surely adding the detail that’s needed to understand how things really work.

This is one of the beautiful things about the mathematics of science. When you truly come to understand the equations, you can see how clearly g, the force of gravity on Earth, is derived from G, the gravitational force of the universe. You can see how the formula for an object traveling at the speed of light is actually just the same as an object moving at an every day speed – it’s just that for every day purposes the complex factors become so small they are irrelevant.

There is nothing wrong with the world without friction. This model is a crucial first step for deeper understanding. It’s the place you have to start, the model you have to truly understand before you can move forward.

It is not uncommon to criticize the social sciences for their lack of a predictive model. Physics can describe the future trajectory of a moving object, why can political science describe the future trajectory of a government.

Frankly, I don’t find that concern all that compelling. I am rather relieved that social sciences can’t predict my every move, and I am dismayed as a matter of principle at big data analytics which seem to move in that direction.

But, from my vantage point far outside these fields, the social sciences do seem to be stuck in – or perhaps, slowly moving out of – a world without friction.

I’ve been glad to see the growth of network analysis within the social sciences. Still in its nascent stages, perhaps, but slowly adding the complexities of reality onto social science models.

People interact with each other. Organizations interact with each other. Organizations, governments, and yes, even corporations, are made of people interacting with each other.

A government doesn’t exist in a vacuum. There is – as we well know – friction within our society. Using network analysis to get at these more subtle interactions is a critical step in moving social science understanding beyond the simple – but valuable model – of a world with no friction.

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Powers of Ten

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You know that amazing 1977 science video Powers of Ten? If you haven’t seen it, go ahead and take a minute to watch it at the link. It might blow your mind.

Okay, well, maybe not, but this was just about my favorite movie when I was in elementary school.

I found myself thinking back to this video today after an engaging conversation with some of my colleagues about the power and role of network analysis.

With the advent of the Internet and especially of social media, the idea of “social networks” has entered – or become more prominent – within the popular lexicon.

These social networks have always existed, of course, but they now seem easier to navigate and quantify. In Facebook terms, I can tell you exactly how many friends I have, and I can also occasionally discover when two people – whom I know from different networks – know each other.

Perhaps more interestingly, the ghost in the Facebook machine has a birds eye view of everyone’s network. Not only am I individually acutely aware of the vast network of people who exist beyond my own, local network, but one could chart the social networks of everyone on Facebook as one giant, global network.

So, that’s pretty cool.

But of course, a social network of this type isn’t the only kind of network governing our world. In a social network, the people are nodes and the relationships between them are edges.

But we could zoom out a level – see where the powers of ten video comes in – and think about a community, not as a network of individuals, but a network of institutions and organizations.

And you could think of these institutional networks at different levels as well. The city I live in has a dense network of organizational ties, but we could also move outwards to look at regional organizational ties, or state-wide ties. We could look at national or international networks of relationships.

We could look at communication networks, transportation networks, relational networks, and many other types of networks operating at these macro levels.

And of course, we can zoom in as well. Thinking of an individual not as a node in a network, but as the network.

In a very literal sense, this could be the network of veins and arteries, the network of nerves, or other biological networks that keep us alive and functioning.

But we can also consider a person’s ideas as a network.

David Williamson Shaffer does this in his work on Epistemic Games. Professional training, he argues, is essentially the process of developing a specialized way of thinking – a network. A lawyer may have to learn many facts and figures, but more deeply, they learn an approach. A way to address and explore new problems.

Not only can you model this networked way of thinking in professionals, you can watch a network develop in novices.

Perhaps an individual’s morals can also be conceived as a network. This is certainly more appealing than concerning a set list of rules to follow – situations are, after all, complex and context in everything.

(While I’ll leave my zooming there, I do feel compelled to clarify that I don’t mean that to imply that we have reached the fundamental particles of human existence. I prefer to think of morals as complex, uncertain things rather than a simple, discrete point.)

So if you zoom in that far, if you consider a network where a person’s ideas are nodes – does that individual network have any connections beyond the person who contains them?

Perhaps.

Ideas are more free than blood cells, and just because I have an idea doesn’t mean you can’t have it to.

An idea may be a node within my network, but I am a node within a human network. I am a node within social networks and I am a node within institutional networks. Local institutions and, ultimately, global institutions, too – though you may not be able to spot my blip on that network map.

And that’s why I like the Powers of Ten video. Because all these different levels, all these different ways of looking at things – they’re not isolated. It’s no accident that atoms make stars.

And it is not only understanding each level that matters, it is understanding how all these levels are connected. How they build to form a whole that looks radically different from its component parts.

Understanding a single network is valuable, but understanding the levels of networks, and the network between them – well, that, my friends, would be a thing of beauty.

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Relativity is a Matter of Perspective

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There’s something that seems soft or overgenerous in saying that everyone’s perspective is valid.

It is, I suspect, the kind of thing that everyone feels they’re supposed to say but which nobody actually believes. Perhaps everyone should get a trophy for participation, but at the end of the day, there is only one Truth. There is still Right and Wrong.

And while I am as struck as anyone by the impulse to define an absolute Truth, the answer is clearly elusive. And, indeed, relative.

In physics terms, for example, the relationship between an observer and an object is critical.

Existence doesn’t happen in vacuum, after all, and understanding Relativity is all about understanding how objects appear relative to each other. This, incidentally, is totally different from the Observer Effect, which demonstrates that observing an object can cause it to change.

If one person is moving near the speed of light and the another person is moving at so-called “normal” speeds, they will see some strange things occurring.

Time will appear to move at different speeds for each party. The faster moving object will appear shorter from the perspective of the slower moving observer.

The beauty about this effect from is that it is far more complex than a trick of the eye. Indeed, you can see the effect foundationally in the mathematics of the universe.

The equation for length contraction, for example, looks like this:

http://upload.wikimedia.org/math/4/1/8/41898d25611a3359aa6bb3a9a7cac36a.pngWhere L is the observed length, L0 is the length at rest, v is the relative velocity between the observer and object, and c is the speed of light.

What you can see here is that there is nothing special about the speed of light per se. That is, there’s not some “normal world” and some crazy “speed of light” world.

Rather, there is a continuous change in length which is entirely dependent on the relative velocity, v.

When an object is moving at the same velocity as an observer, v=0, then the observed length, L, converges to the length at rest, L0. When an object is moving at the speed of light relative to a stationary observer, v=c, then the observed length converges to 0.

It is nonsensical to ask the object’s True length.

There is no such thing as its True length. Only the length as measured by an outside observer moving relative to the object at velocity v.

All lengths, 0 to L0 are equally True.

For every day purposes, we may choose to declare an object’s rest length as its True length. But that is essentially an arbitrary decision. It is the same as declaring that an object’s True length is the length I most typically observe it to be – even if someone else might typically observe a different length.

And here we get back to the challenge of different perspectives in a social science context.

If my observations tell me that one thing is True, and your observations tell you that something else is True, there is nothing at all soft about declaring both perspectives equally valid.

Just like the length of an object, the truth is relative.

Of course, just because the length of an object is variable, doesn’t mean there are no constants to grab hold of.

The speed of light, c, is a constant (in a vacuum) as you may well know.

But c is not a just constant because there is something special about light. It’s not just that there is a maximum speed at which a mass-less object can hurl through space.

Rather, there is a fixed ratio between distance and time. What happens to one effects the other.

If you and I are moving a different speeds and observing some third object, we may see different things. We may observe the object to have different lengths or see time to be passing differently.

But we can understand the difference in perspectives. We can discover the underlying constant and definite the continuum on which both our realities are equally True.

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