Week 3, Summer 2023

The Pursuit of Scientific Exploration

Jun 06, 2023

On Friday, I pondered the question, “Can you check whether a number is prime faster?”

By the end of the day, I had an answer.

Prime numbers. A mathematical mystery. With little to no knowledge about their occurrence or patterns, I didn’t know what I was getting myself into. But the problem seemed interesting enough to think and work on.

So what did I find?

In solving this problem, I discovered that there is a linear relationship between a ‘Number’ and the ‘Number of Primes under that number’. If that sounds confusing, this will help.

Let’s take any random number, like 33. How can I find the number of primes less than or equal to 33 without going through all 32 numbers (excluding 1 since it is neither prime nor composite)?

What I was surprised to find, is that primes have an almost linear occurrence. While you cannot anticipate when the next prime will occur1, you can reasonably predict how many primes you will encounter between two numbers.

This was the “Aha!” moment because, with this conclusion, I could sort through numbers much faster when checking for the validity of a number’s prime.

Based on this trend, I was able to derive a formula that can give me the number of primes smaller than the number. After that, I can find those primes and check whether the given number is prime or not.2

On doing a simple Google search after to see if anything like this has been worked on in the past, I found that our friend - Carl Friedrich Gauss - came to the same conclusion when he was 15!3 I don’t know whether I should feel proud or embarrassed, but I find it to be quite interesting that I unknowingly started working on the same problem that intrigued him as a kid, and, more importantly, even came to the same conclusion as him!

While his formula looks a little different than mine, it still works quite well to predict the number of primes less than or equal to a number.

While I used this conclusion to sort through numbers faster and check for a number’s prime validity, it simply represents a pixel on a display of limitless applications.

It gets me into the realm of Prime counting function and the Riemann Zeta functions…

There is a certain energetic toxicity coupled with working on a new idea. You see it under a light of innocence. It gets you excited. Not knowing any better, it makes you think that you will be the one that figures it out; a concept known as naive optimism.

Coincidentally, Mark Rober talked about it in his commencement speech at MIT4 this year too. If you are looking for the motivation to start something new, something that you have never done before, know that one is never too inexperienced to do something that hasn’t been done before. Naive optimism can, in fact, make you more capable of finding the answer that you are searching for.

This was one of the many things that got me excited this week. So let’s get to the weekly updates!

Music

This week was pivotal for music because I finally found a studio on campus to work in! Here’s what my setup looked like:

It is a phenomenal space with all the tools available for high-quality music production. I consider it quite fortunate to have access to a space like this as a novice. Although I haven’t used any of the software or equipment offered at the studio before, I got around to learning a lot of it this week trying to complete ‘Project Interstellar’.

When I sat down in the studio, I saw the limitless possibilities of what can be made with the tools available here. I was only able to touch the tip of the iceberg this week in terms of what can be done with them. The learning curve might be steep, but I know that the world will look a lot more beautiful once I get to the top of the hill. The summer cannot be a better time to learn to fully unlock the potential of these equipment, and bolster my production skills through continuous effort.

My goal is to make composing music using these tools as easy as using a phone.

Intuitive, quick, and limitless.

Reading

“The conundrum is how to become mature, how to take responsibility and become reliable while at the same time preserving your childlike wonder.”

You guessed it, I got another book from the library this week. Even though I have a couple that I am reading right now (4, to be exact), there is something about starting a new book that I cannot resist.

The book I got this week is ‘India Unbound’ by Gurucharan Das. It is a book that explains the social and economic reforms of India post-Independence.

One of my goals this summer was to understand why India is the way that it is today. How did the wheels that are driving the modern Indian society come to be?

As a kid, I wasn’t interested in this subject as much because it wasn’t relevant to me in any way. But I have started thinking more about it now because I want to be able to contribute to the society’s progress in the near future. And for that, I think it is very important to first understand how things came to be the way they are now.

Since it is a subject I know very little about, it piqued my interest and I am curious to see what I learn by the end of it. In the upcoming months, I will be reading a lot more books to get the context needed to understand the rich political, economical, and historical background of India.

As for the other books I am reading, I am a chapter away from finishing ‘Creativity Inc.’

I have found it to be an extremely rewarding and insightful book, teaching countless important lessons about leading a team, fostering creativity, and, most importantly, unlocking the most creative version of yourself. I will be publishing a separate article with all the takeaways from it once I finish reading it, so stay tuned.

Learning Spanish

It was a pretty normal week for Spanish. I lost access to Duolingo Super so I was back to watching ads and waiting for my hearts to refill before I could continue making progress. sigh.

I was consistent in practicing every night and even found a couple of videos from the TV Shows and Movies that I like, to learn Spanish from their dubbed versions. I realized that listening to someone have a conversation in Spanish is quite effective. I can attest that I am able to pick up certain words here and there.

I just wish Duolingo was faster and exposed me to more new words on a daily basis. Instead of having the same words presented through a hundred different exercises, it should have videos that follow someone using them in a conversation. I’ve found that the more you are exposed to hearing new words, the faster you pick how to use them and in what context.

I am hoping to make more progress this week with slightly more innovative techniques. Still going strong with the streak:

Art

Last week, I read a lot about Art+Engineering. This week, I practiced it.

I finally got back to sketching after a long time. At the start of the week, I made it a goal to go to different parts of the campus and make quick sketches of what was in front of me. So far, this is what I have drawn:

Most of these are very rough sketches with slightly inaccurate proportions, but I intend to get better at capturing live subjects and objects as the weeks progress.

The details of seemingly normal structures start to accentuate when you take the time to observe them closely. Their perspective with respect to the larger whole or the way the sunshine on them changes.

One of my newer goals is to experiment with different artistic styles. Watching ‘Spider-man: Across the Spiderverse’ this week immersed me in a world of artistic beauty. I left the theatre in awe, starstruck by the creativity of the artists of this movie. For me, the creative genuises behind the movie stole the show, not the actors.

I have no words to express the sheer respect and admiration I feel for the people who are capable of thinking so differently and creating something so powerful and unique. They are simple people like you and me who have learned to let their imagination fly and allowed it to manifest itself in beautiful ways.

It is a spectacular movie by itself even before it is an amazing superhero movie. Storytelling is an art, and seeing it done so well is extremely rare.

Don’t even get me started on Animation.

There is so much to learn from them! I wonder how I can adopt its principles to look at the world through a bolder, more colorful, and fearless lens.

I have nothing but immense respect for all animators, thinkers, and storytellers who make movies like ‘Spider-man: Across the Spiderverse’ possible.

It was the most inspiring thing I saw this week.

Wow. Wow. WOW!

Photo of the Week

There are so many cool ideas that I came across this week from Newton’s method of quadratic solutions and Neuroscience to algorithms for finding prime numbers. It was a glimpse into the world of the exciting and unknown. I only wish I had more time to work on everything all at once.

This week was quite energetic and unpredictable. I am only starting to peel the many layers of math, science, history, art, and technology. I have never been more appreciative and grateful of these fields.

I wish I could just keep reading, writing, questioning, and working on a culmination of them all the time. It is tough prioritizing tasks when you want to do everything at once, but it is something that I will have to get better at with time.

I realized that I need to spend less time contemplating the start of something and just start chasing the things that excite me.

So, what are we waiting for?

(*THWIP THWIP* - AND HE SWINGS INTO THE DISTANCE)

Hasta la próxima,
Aaryaman

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