The Laramee Filter: pseudorandom thoughts, subsequently put on the Internet.
Tom Laramee
Date Published:
April 13th, 2024
Word Count:
2,090 (15:00 read time)

Pseudorandom Thoughts on Greenlake (Running the Inner Loop)

In which we consider tasking an alien anthropologist with trying to derive the intended usage rules of the inner loop via observation of it's actual usage.

Around the first of the year, I started to have some wicked problems with my hip flexors. As it turns out, this is a pretty common problem for runners, and I'm fairly certain it's an "overuse / underuse" problem that has arisen from all of the trail running I did late in 2023.

But long story short: I've had to stop running up and have begun, as part of my rehab, running the inner loop of Greenlake, which is flat.

To sum up how I feel about running Greenlake's inner loop, here's a quick thought exercise:

Say we could hire an alien anthropologist to sit next to the inner loop (more likely "hovering a few feet off of the ground [next to the inner loop]"), and asked said anthropologist to try to reverse-engineer the intended usage of the inner loop by watching people actually use it ("...and by all means, take as long as you'd like"), well, what would the alien conclude?
By discerning the usage patterns, well, clearly it should be easy to understand the intended usage rules, yes?

My claim is that no amount of time would suffice, and the alien would eventually throw it's hands up in the air[1], admit defeat, and perhaps retreat to it's spacecraft to leave Earth and never come back again[2]. Why is this?

As far as I know, there are only two main rules[3]:

  1. The inner path is for walkers and joggers.
  2. The outer path is for bikers and skaters.

Simple, right? The paths are well-marked, there are plenty of signs. So, what could go wrong? Here's a quick take on some of the things you'll see on a typical stroll around Greenlake:

In short: there are [literally] no rules of engagement when walking Greenlake[4].

But Honestly: Who Cares About Any of That? (I Sure Don't)

The reason I've written any of this is because I've always wondered, as I'm weaving back and forth across the inner loop going around various dog-walkers, parties-of-four all walking abreast, and big groups of people all walking together:

How much distance does all of this weaving add to my run?

So, I set out to figure out the actual distance I might run if I'm bobbing and weaving my entire run around the lake[5].

Here are my assumptions:

Here's a diagram to help (clickable to make it bigger):

A sin wave, drawn relatively to scale (each block is 1')

The Greenlake path is horizontal and I'm running left to right. The two ellipses represent impediments along the trail, necessitating me running around them to either side. The path is drawn as being 4' wide and I'm running into two impediments every 40'.

(Note: that's just one configuration, I'll do calculations for multiple scenarios)

The Math is Wicked Hard

Now, the underlying mathematics is wicked complicated, and involves a concept known as "complete elliptic integral of second kind"[6]. Here's a reference, though I doubt it'll be of much use.

The high-level solution is stated succinctly as follows:

The General Formula for the Length of an Arc

Now, the proper solution is much more complex[7] (and is thus relegated to the footnotes).

The good news is we don't need that complexity. This problem ("the distance travelled along a sin or cos") has been solved and we can just use the formula and apply it to our problem.

It's also helpful to have access to a tool a tool that will calculate the Elliptic Integral of the 2nd Kind, which we're going to need.

The solution we're going to use is much more manageable, and looks like so:

A Simplified Form of the Arc Length for the Sin Function

Now, that's the length for period = 2π, so we'll be multiplying it by own own [Greenlake] period lengths. And also keep in mind that the final answer is "additional distance above and beyond 2.8 miles".

Note that the "4" comes from breaking the sin wave into 4, equal-length chunks, to simplify things quite a bit.

Below I've worked out three scenarios:

  1. Crowded: two obstacles every 30', using 4' of path width.
  2. Lite Traffic: two obstacles every 50', using 4' of path width.
  3. Worst-Case Scenario: two obstacles every 30', using all 8' of path width.

And before you look at my terrible handwriting, please note the following:

Here are my hand-written calculations working out these three scenarios:

Example 1: Crowded
Example 2: Lite Traffic
Example 3: Worst-Case Scenario
Some Results

Here's a chart of my results. My take-away here is that I probably add around 0.2 miles to each run ... much less when the weather is cold and rainy. It would add a huge amount to the distances (25%) if you actually ran the "Worst-Case Scenario" run.

Total Miles
3.017 miles
+0.217 miles
Lite traffic
2.974 miles
+0.174 miles
Worst Case
3.492 miles
+0.692 miles
[1] Assuming the alien has hands (and holds them up to express exasperation).
[2] Ultimately concluding something to the effect of "This is a planet of idiots and is beyond redemption."
[3] Here are the complete Greenlake usage rules, as indicated by

Green Lake Path Courtesy Code
  • Always show courtesy and respect the rights of other users, and obey signs
  • Warn others when passing
  • Stay on your side of the path
  • Maintain safe speed at all times (10 mph max)
  • Move slowly through congested areas
  • Keep dogs on standard-length leashes (5 foot maximum)
Walkers and Joggers:
  • Use inside lane only (closest to lake) or jogging paths
  • For your own safety, we suggest you walk or run facing bicyclists and skaters
  • Travel no more than two abreast
Bikers and Skaters:
  • Yield to pedestrians
  • Use outside lane only (farthest from lake)
  • Keep right
  • Travel one way only in direction of arrows
  • Bike or skate in single file

[4] Though honestly, I do have my own theory to explain the usage dynamics of the inner loop at Greenlake.
Like nearly all of my theories, this one has no data. This isn't for lack of interest, it's more for lack of time. Personally, I find that there are just too many things in the world about which one should consider, and consider at length, in an attempt to understand them, and there just isn't enough time to give them their due analysis.
And before I offer up said theory, here's a disclaimer: I'm going to be talking about topics like autism and neurodiversity. Because we live in an age where nearly anything and everything can be a source of offense to someone else, let me state clearly that "the neurodiverse" are one of society's most valuable groups and may represent the next stage of human evolution.
(Suffice it to say I'm a huge fan)
So no: this isn't a diss, nor am I making fun of anyone, and nor am I being thoughtless or careless here. I'm just theorizing about why Greenlake is a special kind of anarchy, in terms of it's usage.
That all said: here's my theory:
It begins with the supposition that Seattle is the neurodiversity capitol of the world. This part is wholly unsubstantiated by any data, but bear with me here.
Seattle is a major tech hub, and is home to companies like Microsoft, Amazon, and Boeing. It also has some huge non-tech-centric companies like Costco and Starbucks. But it's the tech that draws the neurodiverse. It's well-understood that neurodiverse employees are recruited by technology companies because their obsessive/OCD tendencies can often produce work of exceptional quality, particularly in areas like software development*. It also well-understood that neurodiverse people seek out tech as a way to blend in**.
So, as a result of all of these neurodiverse tech people moving to Seattle, we're now surrounded by neurodiverse people. If you have kids in Seattle, they have neurodiverse classmates, as well as neurodiverse teachers. Also if you have kids in Seattle, you'll meet, and spend time with, the parents of their friends. You'll inevitably be hanging out with neurodiverse parents. The neurodiverse are extremely well-represented on say, Capitol Hill, which is home to a very rich set of highly diverse people.
Now, neurodiverse people are wonderful, and like I said earlier, may represent the next stage of human evolution, but they do [overall / generalizing here] have some challenges, only two of which I'd like to discuss.
#1. Challenges with full-duplex communication. This is the case with Asperger's Syndrome, in which a person simply cannot understand the effect of their words on the people around them. They also frequently have trouble understanding the intricacies and subtleties of human communication, like eye movement (and eye contact), body language, facial expression, and changes in tone (e.g.: sarcasm).
#2. Challenges with body awareness. This one involves the awareness, or the lack thereof, of the effect your physical body has on the environment around you. Literally, stuff like where you're standing (too close, too far, in the wrong spot) and the lack of awareness of the people around you.
So now think about all of these nice neurodiverse Seattle residents heading down to Greenlake on a nice afternoon to "walk the lake" (as they say here). You can see that there's an inherent propensity for stuff like (1) lack of communication and (2) lack of body awareness and it's effect on the people around you. If you believe my theory, it's easy to understand how the usage of the inner path of Greenlake might be scattered and disorganized, with people mostly in their own [neurodiverse] worlds, not paying any attention whatsoever to the outside world but living 99% in their own heads.
But like I said: it's just a theory.

* What better surroundings could a socially awkward, introverted, nerdy programmer choose to blend in with than at a company like Amazon or Microsoft? ("Oh s/he's just a quirky programmer, don't mind him/her")
** Tech startups are riddled with neurodiverse employees. It's almost a cliche to be a highly-motivated, obsessive, intellectually-excitable, brilliant technologist coupled with a brash, honest, sometimes-hurtful communication style, which in essence I'm describing Aspberger's here and if you work in the Seattle startup scene you've worked with one or more people who fit that description perfectly.
[5] Which I nearly always am, particularly when it's nice out.
[6] Which I won't claim to understand (because I don't).
[7] The proper solution looks a little like so: