Finding Patterns

Image by Author

This post is my early attempt at making sense of human relevance in the age of machine dominance. For my children’s sake.

As a parent of a teenager, I want to make sense of the brave new world we have created — one where AI competes with us in the knowledge economy. I spent a good portion of my non-working hours pondering, with plenty of help to boot. I watched a series of TED talks, listened to many podcasts, read a bunch of books by smart people, discussed with my wife and friends, and reminisced my early teenage years devoid of computers or the internet. I feel better informed to equip my child:

Collaborate, Communicate, Create. Learn to ask the right questions!

AI: Coming of Age

The fourth industrial revolution has brought us Artificial Intelligence (AI). My remembering-self bears witness to four seismic shifts as I approach mid-forties.

  1. Personal computers penetrated homes in the mid-eighties.
  2. The mid-nineties brought us the Internet and the World Wide Web.
  3. By mid-two-thousands, the Smartphone had replaced many verbs.
  4. The AI revolution accelerated around 2015 shows no signs of slowing down.

Many of my age have witnessed three or perhaps, all four shifts. Most recently, the coming of age of AI is rapidly upending our notion of what it means to remain relevant amidst all this disruption. The fourth industrial revolution has no parallels in history. It is nothing like a motor car replacing the horse and buggy at the turn of the twentieth century.

The Machine

Photo by Jordan Harrison on Unsplash

Informed opinions run the gamut. Doomsayers argue it’s snatching away our livelihoods, arguing for Universal Basic Income (UBI). Others find such claims mildly comical. The industry is busy hurtling us toward the AI-first future, even as the debate rages! We all are living through this transformation. A range of TED talks captures this sentiment.

In a contest between human and machine, a human is no match when it comes to memory or knowledge. Sundar Pichai, in his 2016 “AI-first” keynote address, revealed that their knowledge graph held 70 billion facts about people, places, and things. “Google It!” is a thing in our cultural psyche.

What about other uniquely human attributes such as cross-domain general intelligence, values, creativity, conscious experience, emotions, ethics, and morality?

The Human

Photo by Van Tay Media on Unsplash

Maybe far away in the future or this very century, machines may outperform humans in a contest with all the above attributes. Nobody knows. A fascination with numbers informs me such a takeover is going to take time. Compared to humans, it’s hard to judge the intelligence of today’s machines in finding mathematical patterns.

  • Can they develop an intuition for numbers?
  • There is a long list of conjectures in mathematics alone, proposed by humans that span at least three hundred years. Can an intelligent machine conjure one up?
  • What would a mathematical discovery feel like, be it mundane or profound? Would it feel the “Aha!” moment?

It seems to me, today’s AI surpasses human intelligence in solving some categories of problems. Problems with accurate objectives and those that lend well to optimization. For its substrate, it comes equipped with unlimited memory and raw processing power running at incredible clock speeds. It can learn by trial and error, search deep and wide in phase space and compute a vast number of “what if” scenarios in the blink of an eye.

Yet, it’s unclear if it can even match a high school kid’s math skills. To discover mathematical facts, internalize them, find patterns, form associations. Not to mention the thrill of solving a problem, with all its pitfalls, wrong turns, rabbit holes, and the triumphs. To speak nothing of inventing new problems. It is this facet I want to explore. We are good at finding patterns.

Human processing speeds and limited memory capacity pale in comparison with an ordinary laptop or calculator. But we must not be quick to write us off just yet.

The Challenge

High School

I grew up in a lower-middle-class family, by Indian standards. During my high school years in the late eighties, Sir Tim Berners-Lee was busy inventing the World Wide Web at CERN. Yes! that lab of world renown. If my future-self traveled back in time, tapped me on my shoulders, and said I would end up working there, the joke would be on him! We didn’t have a home-phone, let alone a personal computer. Newspapers were delivered to doorsteps and were the primary source of news and entertainment.


I was not particularly into math, let alone recreational puzzles involving math. Its a bit blurry, but that changed when someone, must have been my great uncle, introduced me to Alphametics. Like this puzzle shown below, to be exact.

Alphametic Puzzle: Image by Author

After solving this puzzle, I wondered how someone invented it in the first place. I was thirsty for more, but had no idea of his source. I can’t recall how long the drought lasted. But I ended up spotting another one in a newspaper.

Mukul Sharma was a polymath, a science writer, and an actor who inspired, entertained, and challenged a generation of followers with his Mindsport math puzzles column that appeared in the Sunday Times of India. Solutions would appear the following Sunday. I don’t know all his sources. Perhaps a combination of his own and those he may have collected. Martin Gardner, Henry Dudeney, J.A.H. Hunter, John H. Conway, and others are known for creating such puzzles.

I have long since forgotten all, but one. I struggled all day Sunday. It felt like torture, but I managed to solve it later that evening. It remains etched in my mind for over thirty years! I discovered several patterns, facts about integers that stared at me in the face, almost went unnoticed, but only just.

The Puzzle

Two integers differ by 22. Each, when multiplied by its successor, yields an eight-digit palindrome. What is the smaller of the two?

I tried searching the internet in vain. Perhaps microfiche may exist in some archives. I will use this puzzle¹ to illustrate my point. Obviously decimal system is implied, although one could find solutions in other bases.

What’s The Point?

Can someone using only high school math solve this puzzle? I gave this problem to my teenager and spelled out the following rules:

  1. Only pencil/pen and paper are allowed. Imagine that the internet, the world wide web, the laptop, and all modern electronic gadgets all have disappeared!
  2. No time constraints. Take all the time you need.
  3. Brute force and calculators are not permitted.

The challenge for the machine (or a human plus machine pair) are the following:

How would an AI (algorithm) begin to formulate the concepts, much less solve the problem?

  • How can a human collaborate with a computer in solving the problem without brute force?

Collaborate, Create!

A high school kid is no match for the sheer computing power of a machine that can plow across all eight-digit palindromes and make short work of it. I grant you that. But the challenge lies in building a machine that matches the creativity, algorithmic skills, and pattern-finding ability of a human. I believe we can collaborate. Use creative human ingenuity with its raw power to find patterns! Even come up with new conjectures!

“The opera ain’t over until the fat lady sings!” — Ralph Carpenter

“Robots will never understand the beauty of the game the same way that we humans do” — Lee Sedol

“If you can’t beat them, join them” — Garry Kasparov

“Yes, I will come destroy the computer and defend my species” — Ken Jennings

  1. I will publish the solution and an algorithm next week. I want to give the opportunity for an interested reader to solve the puzzle. Please do not post your answers here or in responses. Thanks!

©️ Venkat Kaushik 2020. All Rights Reserved.