The parallelisms between pumping lemma and life

I have been thinking a lot about this recently, especially as things have calmed down after graduation. There’s a good chance that this might seem very abstract to you (mixing math, linguistics and philosophy does it pretty well) but I genuinely think that there’s something here. Try and read this article slowly if you can.

So, lets get this out of the way.. here is the formal definition of the pumping lemma. I won’t use it the way it’s used in Computer Science classes (majorly to prove/disprove stuff). I just want to take the core idea from it. I promise it doesn’t get any more technical than this:

[Taken from Wikipedia]: For every long enough string in a regular language, there must be a middle section (y) that can be repeated (or pumped) any number of times to produce a string still in the language.

Perhaps it’s easier thinking of this in terms of “loops”. More often than not, if you really look at a process, you tend to see things get repeated over and over again. A process would have:

• the “ramp-up” stage.
• the “main-event” stage [a.k.a., looping/pumping].
• and finally the “wind-down” stage.

You can have different actions in the ramp-up and wind-down stages, but pumping would largely look the same. Ofcourse, any process could have more processes nested inside of it, threads running in parallel etc, but the core idea would still be the same. (We’ll get more into this later.)

Keeping the lemma’s diagram in mind and talking in big-life-picture-terms, I think at this point (esp in your mid-20s), we are at the end of the ramp-up stage. Most of us are done with our education, have a somewhat decent idea of what we want to do professionally, and might even be married. What we are headed for (and very well might be in) is the looping/pumping stage. The next 30–40 years are largely bound to look the same for most people, and the final wind-down stage is up for interpretation.

What I want to get across is that the ramp-up stage was very “happening”. It was filled with major life-altering events. (having a lot of “firsts”, figuring out who we were, literally growing up). Now we find ourselves largely doing the same things and following the same routines in the looping/pumping stage: (work, exercise, cook, clean, travel etc.) New, firsts, and life-altering experiences/decisions don’t come by as often and a lot of major milestones have been hit. A common feeling — after we’ve been around this track a couple of times — is the feeling of “Is this it?!?”.

And here’s the pragmatic answer: it probably is.

The question “What’s the meaning of life?” is a sure-shot way to get a good insight into someone’s perspective. Perhaps the best answer I came across was from Jimmy Carr who responded with “Enjoying the passage of time”. It deeply resonated with me cause of it’s simplicity (and also how well it fits with this pumping lemma thing). We are bound to be spending a lot of time in the pumping/looping stage, and heck, we might as well enjoy it.

What I am going to do now is introduce different things one-by-one to try and make sense of this.

Actions — pumping indefinitely?

At this point, I’d like to introduce you to telic and atelic actions. I’d strongly encourage you to take a moment and go through this brilliant thread by Theresa MacPhail.

Essentially, telic actions have an end in sight and atelic actions don’t. You can be pumping for a while, eventually reaching the wind-down stage (like getting that Master’s degree), or you could be pumping forever (getting better at an instrument).

All this seems well and good, but what gets to me is when atelic actions are taken telically, often by associating happiness with it. For example “Once I reach 10k Instagram followers, I’ll be happy”, “When this reel reaches 500k views, I’ll stop obsessing over it”, “Once I make $200,000/year, I can relax”… I think you see where I am going with this. It doesn’t really feel that different once you reach that goal, does it? It’s always more followers, more views, more money..

“But like with any withdraw, its temporary. The light at the end of the tunnel starts feeling more and more like a torch you’ve been carrying all along.”

- Andrew Rea (Binging with Babish), 2019

The feeling I want to get across is to be more comfortable with the pumping stage, rather than rushing through it to get to the next thing. This is very much like the quote by Ralph Waldo Emerson:“It’s not the destination, it’s the journey.”

Okay, so we are getting more used to this idea. Now, let’s throw time (rather, our perception of it) into the mix.

Time: “the weeks/months/years are just flying by!”

What I find intriguing with the pumping lemma (and a normal person might find obvious) is that you can keep on pumping that same part as many times as you like, and the outcome remains unchanged (the string is accepted, or we go into the wind-down stage). But it sure doesn’t feel that way.

Let’s say someone asks you “how long is a year”. An obvious answer is 365 days. But what a year “feels” like can evoke a different answer based on who you ask:

• for a 1-year old, a year is 100% of their lifetime, so it’s literally forever for them, it’s all they have ever known.
• for a 5-year-old, they’ve seen a few birthdays. A year would be 1/5=20% of their lifetime. [Note the denominator here]
• for a 10-year old, it’ll be 1/10. [Think of the denominator here as a bag of marbles.]
• for a 20-year old, it’s 1/20 [The bag’s growing, but a singular marble is still quite distinct]
• for a 50-year old, it’s 1/50 [The marbles are piling on]
• for a 75-year old, it’s 1/75 [1 marble out of 75 doesn’t seem quite as distinct anymore]

Following the metaphor, note that a marble here still remains a marble, but as we collect more of them, suddenly one doesn’t seem like a whole lot.

What I want you to take away from this is that even though time flows linearly, and a unit of it is immutable, it can very well not feel that way.

Novelty and experience

Another parameter pays a big role here: the novelty of doing something new for the first time. It’s only natural that the novelty wears off the longer (and more frequently) we do something, and the more comfortable we get doing it. (Think of the pumping stage). Now, this is not to say that any of this is a good or a bad thing. It just is.

Let’s take the example of a standard 4-year college experience. Looking back at it, the first year/few semesters were quite “happening”, where everything was new and we were getting used to how things work. As the semesters and years went by, we gradually started getting the hang of it, the classes, exams, events and we had a fair idea of what was in store for the next semester. The initial novelty had long gone. I don’t know about you, but my last two semesters felt like a blur.

And naturally, the longer you do a process, the more experience you gain doing it. The novelty would long be gone — especially for atelic activities — but you gain experience, which is generally regarded as a good thing. The claim that more experience always results in more value is up for debate though.

Parallels

The idea of a subroutine is a rather powerful one. Think of this as a loop in the pumping stage. Here, you know that it’s something that will not give you a lot of surprises, and something you can almost go into autopilot-mode for. Novelty may or may not play a role here, but now it gives us a different view of the pumping stage: a one including multiple subroutines.

Add in doing multiple subroutines in parallel and putting all these things together, all this starts taking a more interesting form for me. You have all these different processes that you do all the time, involving telic/atelic actions, you gain comfort and mastery in certain things, while certain other things bog you down. You learn to handle all of this while trying to push your comfort zone, all while time seems more fluid than linear. (I tried making a diagram for this, but it just got wayy too complex)

Lets consider these examples (you may try and notice the different parts of the lemma, telic/atelic activities, threads, subroutines etc, but mostly I just want to notice how the pumping feels different over time):

• Let’s say you want to learn how to make chicken paprikash. You go out, get all the ingredients and find a decent-looking recipe. Your first time around, it might come off a bit off, or you might miss the mark completely. The next time around, it might come up a bit nicer. After a few more times, it’s almost like you can go on autopilot and make a tight dish without really thinking too much about it. Later on, you can even work on another thing while effortlessly making this dish! (note that consistency in doing it over and over again is a huge part of this.)
• Perhaps something that might resonate with you a bit more is working out. It’s really hard to get started, but there seems to be an “inversion” point, after which things become like a subroutine and it gets easier to build upon it. This quote by the Jogging Baboon from Bojack Horseman sums it up best “Every day it gets a little easier… But you gotta do it every day — that’s the hard part. But it does get easier.”

As you can see, this idea can extend to a lot of things: skills, relationships, breakups, work, travel etc. I hope you get the idea. Something which I haven’t mentioned (but is quite important) is to be able to recognize a lost cause when you see one, and know when to stop pumping.

So, going back to the main question before this: “Is this it?!?”. Like I said before, pragmatically, yes. Perhaps the best way to deal with this is just to develop subroutines, challenge and build on them time and again, and keep trying new things and pushing your comfort zone. This not only keeps the novelty alive, but tremendously boosts productivity.

For me, this whole pumping lemma thing was a nice way to acknowledge and solidify some of my core beliefs. Hope this was helpful to you in some way. I’ll end it here with this quote:

“Shameless consistency is the best kind of consistency.”