So, where do you wanna meet up?
Vis Source: Mike Bostock
I have heard it been said the answer to life is 42 but that does you no good if you don’t know the question. The city provides answers all around you but you don’t know what to collect and where they belong. Standing in Time Square can leave you paralyzed with options but if I told you there was a good bar, well now you have a motivation. Your focus highlights the obstacles, most notably time and distance, and can help you begin forming and working on the question. There is an answer to the question but is this the right solution for you?
There are many options that can suit you, perhaps one best, one that may present you with a future lover, these need not be one and the same. The many wonders are what dazzle the young, the tourists, the romantics, and the imaginative. It is what delights all of us from time to time but this is a passive wonder done to you. It asked nothing of you and is unaware of your presence, would happen without you, and probably wouldn’t be influenced by your presence. A question provides purpose, perspective, a point of you. The rest may still apply, especially your non-relevance, but a narrative has been intentionally focused and now you choose to some extent the pictures that get framed. The bar, the beers, they are temporary. The process is a tool. It’s applicable to other solutions. Use it, work your decision muscles, and build your narrative skills.
“You take delight not in a city’s seven or seventy wonders, but in the answer it gives to a question of yours.”
Every couple of weeks I grab a pint with a particular friend of mine and catch up. Hopefully you too have someone to share stupid and serious ideas with. Someone who appreciates your sensibility and opinion but does not take you too seriously and is not shy to call you out on your shit. Most importantly, someone who can hold an interesting conversation, be occasionally irreverent, and have a laugh over a good beer.
In New York there are a ton of options for grabbing a good pint, especially with the rotating taps at most self-respecting places. If you work in The City1 odds are you’re either in Midtown or the Financial District. If you enjoy good beer, and less of a bustling afterwork crowd, chances are you won’t stick around long in these neighborhoods, unless you’re with your work colleagues and kicking back a few, unwilling to be the douche that makes everyone else accommodate his beer snobbish palette by going to some less than office-convenient bar. Don’t be that guy. At least have some finesse and teach people slowly about what good beer is and entice them that way over time. Make it seem like it’s their decision to go to “that bar with the weird but delicious beers”.2
Depending on the choice of bar, and this is determined by a litany of considerations: convenience to work/home, newness of establishment, available grub, and of course beer selection, there is then the logistical matter of getting your ass from the office chair to the bar stool. Subways usually (nearly always, really) play a role and then there is the most time honored New York means of travel, walking. Tourist or resident, you can’t help but notice the importance and etiquete of walking in The City.
I like to play a game I call “Shark Walk” where if you stop moving you “die”. The goal is to get from A to B without waiting at a light. Besides jaywalking, also a NYC tradition, and running to beat traffic, preferably avoided,3 your best bet is knowing your options, staying alert to traffic lights, and minding your pace. It’s always preferable to “pick it up” a bit or lay back with the pace to standing at a corner waiting for car traffic to pass. And this is not jogging, so running in place does not count.4
This game is applicable to lunch hour walks, taking a stroll (can you say flaneur?), or making your way from the subway stop to the delicious pint waiting for you at your watering hole of choice. If you want to keep moving and give yourself the impression that you’ve got some little bit of control in this maad city then know your options. Which brings us back to the topic at hand, how many ways are there of getting from here, thirsty, to there, imbibing?
A Simple Example (credit to the MTA)
Despite subway deserts, that you can attempt to alleviate, the MTA covers NYC reasonably well. In Manhattan at least it is difficult to be more than a 15 minute walk from subway station to destination (whether you’re willing to make the necessary connections to get to that most close station is another point entirely).
Assume you’re on the Sixth Avenue line and get off at 34th for the purposes of getting a drink at a certain U2-named bar, that places you two blocks away from the corner of 33rd & 5th (let’s ignore the difference in avenues and streets, since it won’t matter either way in our scenarios) which requires you to go east and south, in either order. Since both options are available you have two routes to getting there.
Now if you’re two blocks up the Avenue from your destination, 35th & Fifth Ave, the same number of blocks (again not in actual distance), you only have one choice, walking downtown.
Data Source: Google Maps
Intuitively, being off of a straight line provides alternate ways of getting to the same destination and this is especially clear in The City, or an area of a city that is laid out like a Cartesian plane (we will be ignoring bisecting streets and avenues, such as Broadway).
Second intuition, when it comes to a straight line it doesn’t matter how far out you extend it, the most direct way of getting to the destination remains the same; you have one best option, you actually have a best option. Straight ahead.
“An invisible landscape conditions the visible one”
Final intuition, the more blocks off of a line between you and the bar in a grid layout, the more options. Four blocks away, in a 3x1 fashion, say starting on 36th and Sixth and still aiming for RnH East you have no less than four ways of getting there (either taking Sixth to 33rd and heading east or heading to Fifth at 3 of the earlier options: 36th, 35th or 34th, and continuing downtown). The options increase if you happen to be in a 2x2 grid, though still four blocks away in total. Can you envision in your mind the routes available to walk from 35th and 7th to 33rd and Fifth? I’ll give you a second.5
“Futures not achieved are only branches of the past: dead branches.”
As I said above there are a ton of options in the city, with some neighborhoods more blessed than others. In this section of Midtown we can hit the U2 album-named bar or the Irish novel pub, each of which have dozens of taps and dozens of more bottles available. Between the constant rotation and occasional brewery tap takeover there’s always something new to choose from, but this doesn’t always mean there’s something new to you. Perhaps one of these places has just one new beer you care for, maybe not even a new one but a particular flavor for the day (I don’t believe in favorite beers, what are we 12? Bad example, you shouldn’t drink kids). The other bar has nothing you expect to blow you away but there’s a new brewery you’ve never tried before, perhaps it just started distributing in your area.
Of course, what’s stopping you from going to both bars, or more, and drinking it all? Hmm, … time, money, kidney functionality, tomorrow’s hangover; fear of losing your wallet, your balance, walking ability, bladder control, ability to get it up; the desire to hold down a conversation, hold down a job, hold down your dinner; getting home safe; not getting someone pregnant, not getting it up; avoiding a fight, the cops, an ill-advised booty call, drunk idiots; your credit limit, ability to remember your pin code; the expiring unlimited metrocard; the dying cell phone battery in the shitty bar that doesn’t have a spare power cord, outlet, adapter, whatever; your patience, your temper; the bringing down of the walls to the self, opening up to the universe and realizing the meaninglessness of it all.
Mr. Euler, I Presume
Project Euler offers a canonical set of mathematical problems to challenge both math and computer programming concepts. One of these problems deals with Lattice paths and is the springboard for this thought exercise. Remembering nothing beyond my fourth-grade math but intuiting there’s got to be (and 4th grade grammar, apparently) a systematic way of solving this mystery (duh - 4th grade humor, too) I go first for a visual representation.
I take the origin coordinate (0,0) and branch out to see how the numbers expand looking for a pattern. This is easy enough to do with a 1x1 and 2x2 grid but begins to present problems at 3x3. I rush to develop the last of these trees, am sloppy without realizing it and then spend 30 minutes attempting to find a pattern to an incomplete “solution”. Upon returning to my sketches, and revisiting my steps, I realize my error.
“they must admit that all their calculations were wrong and their figures are unable to describe the heavens”
I correct the path count and redo it from scratch on the other side of the page to confirm the result. Convinced of the correct next path count I try again to find a mathematical pattern. Nothing doing, I figure more numbers of paths would help but do not necessarily trust myself to come out with the correct path count of the 4x4 grid.
Had I been at this corner before? Did I go right or down last time? Why can’t I remember, there are only two directions to keep track of? Sure to be incapable of keeping it straight in my head I envision the scene from Inception where the city folds in on itself or an Escher drawing. What’s a fool to do?
How about building an equally foolish function, but one that knows how to keep count? That would help put off losing my mind a while longer. Done.
Now armed with path counts for square grids of 1 to 4 blocks6 I sense that the mysteries of the solution are shortly to be revealed. After another half hour it’s clear the revelation will be taking its time and may require another visual representation, this time listing out the number of paths available at each corner of the grid. I start simply and build up, taking my time and hoping that my deliberate attention will clue me into following the right direction. And what do you freaking know? By the time I expand from the 2x2 to the 3x3 I’m seeing a possibility. Having the next path count at 4x4, presumably the correct one, allows me to know what to look for and validate the pattern further. As soon as this next step returns the right number I expand my efforts from a sheet of paper, to an Excel sheet, and finally to a slightly less foolish function.
“Elsewhere is a negative mirror. The traveler recognizes the little that is his, discovering the much he has not had and will never have.”
From the very beginning, with the simplest example of a 1x1 grid, you’re made aware of splits in the journey, the need to choose in order to continue moving both in the world and through the problem at hand. Sticking with square grid arrangements should make it clear from the first fork in the road that anything we do further down the road, all the other branches we’ve opened up by going left instead of right from the very beginning have a twin should we have gone right instead of left at the start. The route splits in two and every branch afterwards has a double. This allows us to first split the problem in half, get a partial answer, and afterward confidently multiply by two to arrive at a solution.
When I’m in the process of developing a routine related to a new location, whether for school, work, or a doctor’s visit, I prefer to map it out in my mind ahead of time and choose among two options if possible. As I return to the location I remember previous paths taken consider if there is a more efficient one, not just shorter, a less noisy one perhaps, a way of getting there that incorporates awnings or atriums, beautiful options for rain or when it is too hot. The process repeats itself later in the day for the journey home, but the result need not be a duplicate in reverse. The day is difficult, it may be night depending on the time of the year, and my considerations are usually different. Is there a park to walk through, somewhere to see the riverfront, is there a favorite building in the area? Sometimes I take redundant turns to my destination in order to introduce randomness.
Initially I had focused on just one branch of paths, knowing the number could be doubled to reflect the paths branching in the alternate direction. In creating an Excel representation of my hand notes the whole numbers jump out at me and I realize on closer inspection the number I require can be had with no additional arithmetic, even one capable by my fourth grade talents.
We now have a simple and elegant way of calculating the path counts.7 It’s unlikely for all of these options to be needed in getting around but they’re helpful in keeping you free and flexible in your walks, to the bar or somewhere else less appealing. Just remember to be careful on your way back. With a little alcohol these numerous options, and more depending on your augmented imagination, have a way of making their presence felt, creating confusion, and then we do have to worry about walking in any of four directions (N, S, E, & W). At that point, though you’re within a grid you’ll be walking in circles, unable to escape the nexus of the universe.
To the Bar!
You have momentarily left your place of work and your day-to-day responsibilities behind and are now focused on the meeting a friend. Even if not foremost in your mind, ideas that you have meant to share now begin to bubble to the forefront. In anticipation of this meeting feelings of past meetings provide a setting for what do you expect to transpire. The city is layered with many stories, yours included, the friendship is similarly interwoven and tonight a new thread will be added.
The city streets are the material, our lives the paint, and the innumerable coats we apply help to layer the environment so that what remains in our mind is more than just the physical, the visual. We see with our eyes the objects in front of us and these are imbued with meaning by the relationships we have cultivated with and around them. Our actions develop a spiderweb, the city’s grid provides the joining places for these threads. The spiderweb is extended in multiple directions and dimensions. Seemingly unconnected events of time and space are still yet intertwined by the relationships created through the comings and goings of this city’s denizens.
“The city does not consist of this, but of relationships between the measurements of its space and the events of its past:”
I’m walking down the avenue, walking a bit slower than usual. Work is out and I’m letting myself be taken by the flow of the other people on the sidewalk. If I were headed to Grand Central or some other major afterwork hub I might be stampeding along with all the others, but this is not a major artery, people are more relaxed. No need to rush. I could get to the pub first but that would only mean I would have my first pint alone, perhaps making small talk with the bartender or another patron. Undoubtedly the pint would be half done by my friend’s arrival and where would that leave us? Our rounds would be off, throwing the drinking and comparison off kilter for no good reason. Sure, we could double up on a particularly pleasant pint but something about today tells me to lay back.
Work has been chugging along, nothing particularly interesting to talk about there but, sticking to the theme, there are the ever present issues of the economy, globalization, the future of work with respect to automation, and any number of new gadgets or their implementation (you see the drone video over Chernobyl, yet?). Approaching a crosswalk the late afternoon sun rains down through the buildings momentarily requiring I squint. The eyes narrowing distorts my vision and adds to the diffusion of images by the sunlight. The warmth on my face feels good and contrary to what I said previously I decide to wait on the side and take in the moment, closing my eyes for a bit while turning my face even more toward the sun. All I see is a dark red, the surrounding sounds are muted, and I think of having a light-style beer.
“Desires are already memories.”
It’s the end of summer, a Weiss beer wouldn’t be out of place. How about a sour? Also a good style for the final warmth of the day and a fun way to wash away the final touches of humidity. Two months ago the heat could feel like a blanket now it’s just a warm wind from time to time, the coolness on the skin taking over after it passes. Traffic is coming to a still and I wipe lightly my upper lip with the back of my hand. Though there is no sweat there it’ll be another week before I disabuse myself of this summer habit. Suddenly I don’t mind so much having a beer while awaiting my friend. I did get off a stop early in order to kill more time and get a little movement in before the sedentary activities of tonight. At least our minds and voices will be active, for a time anyway. After a couple of IPAs, perhaps a smoked beer, definitely an Imperial Stout, and maybe even a season-creeping offering our minds will also have a head start on sedentary activities. The anticipated brews fall into the pattern of past encounters, even the conversations while unpredictable in their detail will be familiar, like seeing a favorite athlete or sports team performing.
Data Source: Project Euler, if you're clever enough. Ha!
All indented quotes above come from Invisible Cities by Italo Calvino.
1 That’s right, I capitalized it. ↩
2 What’s more important in the end: the credit or the beer? ↩
3 And never a good look. ↩
4 Ibid. ↩
5 It’s six this time. ↩
6 1x1: 2 paths; 2x2: 6; 3x3: 20; & 4x4: 70 ↩
7 Even without the initial benefits of relying on binomials or Pascal’s triangle directly. Like I said, 4th grade math. ↩