Walking to work

My commute to and from work each day consists of a train and subway ride, as well as about 1/2 a mile of walking. This time is when I get most of my reading, writing, and thinking done. Unsurprisingly, given how much time I spend missing trains and held up walking at red lights, my thoughts often turn to the walk or ride itself.

Let’s consider one part of my commute: the walk from the PATH station to the office. This walk is about 5 blocks or so on the New York grid, passing through a traffic light at each intersection. Plotted with one dimension of space and one of time, it might look like this:

In this plot, time progresses from left to right, and my walk will take me from the top of the plot (the train station) to the bottom (the office). Each red light along the way is indicated as a red line (green lights are left blank for clarity – they would fill the blank spaces between each red dash).

Let’s say I leave the train station at a particular time near the left side of the graph and start walking:

Assuming I walk at a constant speed, my path while walking looks like a diagonal line through time and space. When I get held up at a red light, my path goes horizontal (I’m standing still in space, but still progressing through time). Overall, this gives my path a bit of a zig-zag pattern in the 1-D space + time plot.

Now, on the same morning, let’s say I leave the PATH station minute or two later (maybe the train was delayed a bit, or I exited from the back of the train instead of the front):

Once again, my zig-zag path takes me to the office, stopping at the red lights along the way. But interestingly, despite leaving later from the train station, I arrive at the office at exactly the same time:

In both routes, despite stopping at different lights early on my journey, I still get caught at that same last red light. It didn’t matter that I started earlier or later – the outcome was the same.

Now, we plot all of the possible starting times and their resulting walks:

Interestingly, despite dozens of possible starting times at the train station, there are only a few possible times of arrival at the office. In effect, the red lights “collapse” the outcomes into a smaller set. For example, the 18 different starting times highlighted in the figure below all have the same result:

Another interesting set of paths to look at are the “tipping points” – any pair of neighboring paths with different arrival times:

Here, a difference of a few seconds in starting time between the blue and yellow paths means many minutes of delay on the arrival side. Also notable is that the blue path is one of the shortest, with respect to total time, whereas the gold path is one of the longest.

Next time: how I think these paths relate to chaos theory and strange attractors

(Inspired by Ybry’s visualizations of train schedules, from Edward Tufte’s book Envisioning Information.)

Book: Einstein’s Dreams

1905, known as Albert Einstein’s “annus mirablis,” saw him produce some of the most inspired work in the history of natural philosophy. From the outside, it is easy to see the import of this work – in a single year, Einstein established whole new fields of study, including fundamental discoveries in quantum physics and the special theory of relativity.

But what was it like on the *inside*? What was it like to *be* Albert during that year, the Swiss patent clerk discerning the true nature of the universe in his spare time? What is the essence of scientific discovery, of seeing so deeply into fundamental truths, of “Eureka!”?

Alan Lightman’s beautiful novel Einstein’s Dreams brings us inside the thoughts of this most famous of scientists through a series of meditations on the nature of time. Imagine time as a stream, “occasionally displaced by a bit of debris, a passing breeze,” or time flowing backwards, or a single place where time stands still. Imagine a world where time flows more slowly for those at higher altitudes, where everyone lives in the mountains on houses built on stilts.

In “a world in which people live just one day… [where] a man or a woman sees only one sunrise, one sunset.” December babies live a cold life, while June babies only know warm. Those born at night tend to be insular, not venturing outdoors even when daylight finally breaks, while those born during the day become depressed in the literal twilight of their lives.

Written in short chapters with brief sentences like brushstrokes on a painting, Einstein’s Dreams is an exercise in “What if?” – much like scientific thought itself. Each chapter takes as its premise some new truth about time, using it as the basis for a meditation on love, loss, relationships, life, and death. In the world without memory, lovers find that every night is the first night of passion. At the point where time stands still, mothers refuse to let go of their children, staying where “the beautiful young daughter with blue eyes and blonde hair will never stop smiling the smile she smiles now, will never lose this soft pink glow on her cheeks… will never think thoghts that her parents don’t know, will never know evil.”

But beyond the meditations on time, I found the interludes, describing Einstein in the Zurich of 1905, to be even more fascinating. Here is Einstein walking slowly down Speichergasse with his friend Besso; here is Einstein absentmindedly staring off into space during dinner; here is Einstein sitting in a fishing boat, looking for shapes in the clouds.

I’ve been fascinated by biographies and portraits of great scientists since I first read Genius, James Glieck’s fabulous portrait of Richard Feynman. What is it that makes these great thinkers tick? Why do they see deeper or farther into the truth of the universe than the rest of humanity? How do they discern this truth, and how do they manage to convey it to the rest of us? Einstein’s Dreams is another fantastic portrait of a great thinker in his prime, seeing what no one else has seen.

First Post!

I figure an endeavor like this deserves some sort of introduction to
get things started. A bit of a “Who, What, Why…” sort of thing.

First, the who – you can read more about me here.

What? I tend to be interested in physics, biology, neuroscience,
artificial intelligence, computer science, scientific histories and
biographies, science fiction, and hell, pretty much any book that blows your hair
. Incidentally, the title of the site itself is a play on
words regarding the possibility of man creating another intelligence
in the world.

As to why, mostly, this blog is a way for me to get my thoughts down –
to work through things I’ve been reading, thinking, and taking notes
about for many years now. I expect it to be a bit scattershot, but I
also think that’s going to be half the fun.