Solomonoff Induction

Imagine that you are given the following set of numbers and you have to predict the next one:

2, 4, 6, 8, ___

Did you guess 10? Why? Probably because that’s the simplest pattern — “add two each time”. But consider this alternative explanation — “Add two every time until you reach 8, then suddenly switch to adding five”. Then, the next number would be 13.

Both explanations match the observed data. Yet, intuitively, you’d bet on 10 because it’s simpler. But why exactly does simplicity feel right?

Simplicity feels right because of Occam’s Razor: “Among competing hypotheses, choose the simplest one”.

Then, in 1960s, Ray Solomonoff had a brilliant idea. He decided to represent each possible explanation (or hypothesis) as a computer program. The shorter the program length (in bits or complexity), the simpler the hypothesis.

For example, there are several computer programs to decide the next number in our series 2, 4, 6, 8, ___:

Program	Length (in bits)	Interpretation
Print all even numbers	Short	Simple, general
Print 2, 4, 6, 8, then print 13, 18, … (add 5 to last number)	Medium	Complicated, special-case explanation
Print numbers 2, 4, 6, 8, followed by random unpredictable numbers	Very Long	Highly complex, arbitrary, no clear pattern

(While Kolmogorov complexity—the length of the shortest program that generates your data—is a powerful theoretical idea, it’s actually uncomputable in practice, so we use description length as an ideal guide for simplicity.)

The shortest program often has the simplest interpretation. Supervised learning algorithms are attempts to compress all available information in data useful for decision making into simple binary. Solomonoff said that to predict the next event, we should:

1. Consider every possible program that could produce the observed data.
2. Assign probabilities based on simplicity:
   1. Shorter program → Higher probability
   2. Longer program → Lower probability
   3. \(\text{Probability} \propto 2^{-\text{program length}}\)
3. Predict the next event by taking a weighted average of the predictions from all programs.

In other words, we can imagine an infinite “multiverse” of programs generating your data. We don’t just pick one; we average over them all, weighing each according to simplicity.

Even though practically it is impossible to use, it guides us to understand that simpler algorithms that compress data better are almost always better representations of data. Additionally, since Solomonoff induction relies on an uncomputable prior, real-world machine learning uses practical substitutes like Minimum Description Length (MDL), Bayesian model averaging, or ensembling to approximate the idea of weighing simpler explanations more heavily.

Multiverse?

Now, while exploring Solomonoff induction, I stumbled upon its intriguing connection with another concept: the multiverse. Physicist Max Tegmark proposed four levels of multiverse, each level capturing a different kind of parallel universe.¹

The first level Tegmark describes includes regions beyond our observable cosmic horizon. Essentially, these universes are extensions of our own, governed by the same physical laws but possibly differing in their initial conditions.

The second level imagines universes arising from something called eternal inflation (recall that because of cosmic inflation our universe is constantly expanding), each potentially having different physical constants and laws of nature. Solomonoff induction would, in theory, incorporate these universes too, evaluating them based on how simple and computable their fundamental rules are.

Shorter, simpler descriptions (or programs) of universes would be considered more probable than complicated, special-case scenarios.

The third level relates directly to quantum mechanics, specifically the many-worlds interpretation. Here, every quantum event creates branching universes, each representing different outcomes. This concept resonates strongly with Solomonoff induction’s approach, where each potential future event is considered simultaneously, weighted by simplicity and computability. Each “branch” is akin to a different program output, contributing to the overall prediction.

Finally, Tegmark’s fourth level—the “ultimate ensemble”—is the broadest and most abstract. It suggests that every mathematically consistent universe that can exist does exist. This level again matches perfectly with Solomonoff induction. Since Solomonoff induction evaluates every conceivable computable hypothesis, it inherently encompasses this idea, assigning probabilities to these universes based purely on the elegance and simplicity of their mathematical description.

It’s worth noting that in quantum mechanics, the many-worlds interpretation assigns probabilities to outcomes using the Born rule, not by simplicity—so the analogy with Solomonoff is more metaphorical than literal. Also, eternal inflation refers to the ongoing creation of new “pocket universes” with different constants, while the current expansion of our universe is driven by dark energy.

Okay, but how is this related to language models?

Bringing it back to language models: when models like GPT-4.5 predict text, they’re essentially compressing huge amounts of information into compact representations—similar to the spirit of Solomonoff induction. Training methods like cross-entropy loss connect to Minimum Description Length, rewarding models that capture patterns efficiently.

When sampling outputs, techniques like temperature scaling and nucleus sampling let us explore a range of possible continuations, almost like averaging predictions from multiple “programs” or hypotheses. In practice, ensembling and mixture-of-experts architectures mimic the idea of averaging over many models, echoing the theoretical blend of simplicity and diversity that Solomonoff induction imagines.

Is Multiverse Real?

We don’t know. But as a fan of “Everything Everywhere All at Once”, I would totally say “Yes!”.

History of Albania

The territory of modern-day Albania was inhabited in classical antiquity by various Illyrian tribes. Between 200 and 400 BCE, Greek colonizers established trading posts along its coastline, most notably in Durrës—a beach town near present-day Tirana. Following the Illyro-Roman Wars (229–168 BCE), the region was absorbed into the Roman Empire. After the empire’s division in 395 CE, Albania came under the Eastern Roman (Byzantine) Empire.

In 1444, the Albanian nobleman George Kastrioti—better known as Skanderbeg—united feudal lords in a military alliance to resist the advancing Ottoman Empire. Skanderbeg, now celebrated as a national hero with the main square in Tirana named after him, held off Ottoman forces for over two decades. After his death, and within a decade, Albania fell under Ottoman rule. Yet the sense of national identity he forged left a deep and lasting mark on Albanian nationalism.

Skanderbeg Square, Tirana, Albania.

As the Ottoman Empire weakened, Albania declared its independence on November 28, 1912. The next two and a half decades were tumultuous, marked by the reign of two kings and occupation during both World Wars. These events eventually set the stage for Albania to become a socialist (“Stalinist”) state under Enver Hoxha, the First Secretary of the Labour Party. From 1944 until his death in 1985, Hoxha ruled Albania as a rigid, Stalinist one-party regime defined by forced collectivization, state-enforced atheism (making Albania the world’s first officially atheist country), and extreme international isolation.

Stalin’s death in 1953 and Khrushchev’s speech “On the Cult of Personality and Its Consequences” denouncing the Stalin’s methods in 1956 alarmed Hoxha.¹ He viewed de‑Stalinization as a betrayal of Marxism‑Leninism. By 1961, Albania formally split from the USSR, expelled all Soviet advisers, and joined with Chairman Mao’s China as fellow anti‑revisionists. Through the 1960s and early ’70s, Albania received Chinese economic and military aid.

But as Mao’s successors began opening China to foreign investment and rapprochement with the West (notably Nixon’s visit in 1972), Hoxha denounced China as “revisionist” as well. By 1978 all Chinese personnel were gone, and Albania embarked on its “self‑reliance” policy. From then until his death in 1985, Hoxha presided over Europe’s North Korea.

He persecuted religious institutions, banned almost all private enterprise, and enforced strict travel restrictions. His regime executed or imprisoned thousands deemed opponents, and Albania became one of the most repressive states in Europe. For more on this and other historical stories of Albania, one should read Lea Ypi’s “Free”.

The list of “tortures” done during Enver Hoxha’s regime are horrendous — FAIR WARNING. “Strapping dynamite on the body”, “burning of sexual organs with petrol”, “putting inside the coffin alive”, “crushing breasts with pliers”, “cat with claws put inside underpants of women and then hit with a wood”. These are beyond hurtful.

36 Types of Tortures Committed By The Investigator During The Regime. Courtesy: “House of Leaves” museum.

Upon Hoxha’s death in 1985, his successor Ramiz Alia cautiously introduced reforms under pressure from domestic unrest and Gorbachev’s Soviet policies.² By 1991 multi‑party elections had been held, and in March 1992 the center‑right Democratic Party assumed power, marking the end of the communist system. The 1998 constitution enshrined rule of law and human rights. Despite severe economic collapse and the 1997 crisis, Albania stabilized in the early 2000s, joined NATO in 2009, and is now an official candidate for European Union accession.

How is Albania Today?

Today, Albania is a modern European nation, home to many beautiful attractions and stunning beaches. I was fortunate to be hosted by my friend Dea Bardhosi, who, along with her sister Keti and their parents, generously showed me around the cities of Tirana and Durrës. Here are some highlights from my trip.

Dea Bardhosi and I at the friendship monument in Tirana.

I landed at Tirana’s Nënë Tereza Airport (Mother Teresa Airport, TIA), which has direct connections to major European cities such as London, Paris, Munich, Frankfurt, and others, as well as flights to and from Dubai. The airport is named after Mother Teresa, the renowned Catholic nun known for her service to India’s poor and sick. Interestingly, although I always assumed she was Indian, she was actually Albanian by birth and became one of the first foreigners to acquire Indian citizenship through naturalization. Despite her iconic status in Albania, Mother Teresa remains somewhat controversial in India, where she has been criticized for her practice of withholding anesthetics from patients, stemming from her belief that suffering brought one closer to God.

Local Food in Tirana

I had the pleasure of sharing a traditional lunch with Dea’s family, and the local food was delicious. We enjoyed goat shoulder, a platter of traditional Albanian dishes, and finished with flan accompanied by their classic espresso. The meal was made even more memorable by the setting—at the top of the Dajti Mountains, which you can reach from Tirana by cable car (except on Tuesdays).

Beachtown: Durrës

Durrës is the second-most populous city in Albania, after Tirana. It’s actually older than Tirana, having been a significant center during both the Greek and Roman eras. The city is also home to an ancient Roman amphitheater, which—while smaller—bears some resemblance to the Colosseum in Rome.

The beach at Durrës is very clean, though quite shallow; the water near the shore barely reached my shoulders, at about a meter deep. The sea is clear and the waves are gentle, making it ideal for swimming. I thoroughly enjoyed my time in the water with Dea.

Liquor to Try: Raki

Albanian raki (raki rrushi, or simply “raki”) is a strong fruit brandy that has been distilled in rural Albania for centuries. The recipe varies by region: northern Albania typically produces grape-based raki (raki rrushi), while in central and southern areas, you’ll also find plum (slivovica), apricot (kajsie), and pear (dardhë) versions.

I picked up a bottle at the duty-free in TIA airport on my way back and have enjoyed it both as a shot and mixed into a cocktail with lychee, lemon, and sugar.

Conclusion

My week in Albania gave me far more than a checklist of sights—it offered a window into a nation reshaping itself after decades of isolation and upheaval. Tirana’s colorful streets, Durrës’ ancient ruins and gentle beaches, the warmth of Albanian hospitality, and the taste of local food and raki all left a vivid impression. Albania is still carving out its place in Europe, balancing old wounds with new energy and optimism.

If you’re looking for a travel experience that’s both welcoming and thought-provoking, Albania is well worth a visit. I’m grateful to Dea and her family for making me feel at home in a country still discovering itself—and I look forward to returning someday.

Passport Through the Ages

Although the concept of modern passport is only a post World War II event — mostly to avoid espionage and identity verification in porous boundaries of the European countries — passports as documents asking for safe passage are very old. One of the oldest instance is found in the Hebrew Bible (Nehemiah 2:7–9, 450 BCE) when Nehemiah, an official serving King Artaxerxes I of Persia, asked permission to travel to Judea; the king granted leave and gave him a letter “to the governors beyond the river” requesting safe passage for him as he traveled through their lands.

In ancient India, Arthashashtra (3rd century BCE) describes duty of Mudrādhyakṣa (lit. ‘Superintendent of Seals’) who must issue sealed passes before a person could enter or leave the countryside. Ancient Chinese kingdoms like western Han kingdoms issued passports (傳; zhuan) and it determined a person’s ability to move throughout imperial counties and through points of control.

Here are some old passport images, courtesy Wikipedia.

First Japanese passport, issued in 1866

Chinese passport from the Qing dynasty, 24th Year of the Guangxu Reign, 1898

An Ottoman passport (passavant) issued to a Russian subject dated July 24, 1900

World War II Spanish official passport issued in late 1944 and used during the last six months of the war by an official being sent to Berlin.

Another fun fact: With fewer than 800 citizens, Vatican passports are among the rarest—and virtually every holder is either clergy or a Swiss Guard.

Beautiful Passports

While my Indian passport is pretty ordinary (pun intended), there are several countries whose passports are a delight to look at. For example, the Australian passport has hidden images that only show up in UV light, with even the thread acting as Aborginal flag!

Hong Kong’s passport is a marriage of old world artistry and their futuristic skyline.

New Zealand’s passport is a beautiful tribute to all the explorers who discovered this beautiful nation, intricately tying Maori designs with modern ones.

Switzerland’s passport shows each region’s topography map under UV light.

United States’ passport features the country’s founding principles. Each two-page is marked with a quote from a historically-important-person. It is also the only passport I’ve see which comes with eight pages of usage guidelines.

The Turkish passport includes local flowers under UV light and historical buildings under any light.

Source: The Most Beautiful Passports in the World: Regula’s Pick (2025)

Allow Bearer to Pass Freely

While most passports request the border officials inspecting the document to “let the bearer pass freely”, it isn’t always the case. Not all passports are equal. Some passports, like United Arab Emirates (UAE), Japan and Singapore, are welcomed by almost all countries. Others, like Afghanistan and Pakistan, require a visa by almost all countries. Thus, I wanted to explore how “powerful” each country’s passport is.

There are several ways to measure how “powerful” a country’s passport is. Consider India as an example.

1. Visa-free: The number of countries that an Indian national doesn’t require a visa to visit. 30 countries allow visa-free access to Indians. Singapore leads this measure with visa-free access to 137 countries.
2. Visa-on-arrival: At the port of entry, many countries grant easy visa to an Indian national. 45 countries give visa-on-arrival to Indians. Australia and Peru lead this measure with visa-on-arrival access to 54 countries each.
3. Land Power: The percentage of earth’s surface that an Indian national can visit. Indians can visit 34.5% of earth’s landmass. Spain leads this measure with access to 88.4% of earth.

The infamous Henely Passport Index has slightly different methodology: it uses proprietary information from International Air Transport Association (IATA) Timatic database which also provides essential travel information to international airlines. They don’t count e-Visa towards free travel which another (more user-friendly) tracker Passport Index does. Consequently, there are minor differences in the ultimate results.

However, it is clear that there are some countries that enjoy free travel in more countries than others. So, that begets the question — what countries’ passports are more powerful than others?

Powerful Passports

To answer the question, I calculate a “Travel Easy Index”, which is simply the count of countries that let you in easily (visa-free or visa-on-arrival including e-TA). Data is sourced from the Passport Index website and World Bank for GDP Per Capita (PPP).^{2 3}

When we map out global “Passport Power”, we’re really charting the footprint of a nation’s diplomatic reach, economic heft, and reciprocal trust agreements. At the top of the list you’ll see Japan, Singapore, Germany, each offering their citizens visa-free access to well over 180 destinations.⁴ These passports earn their strength from decades of stable foreign policy, participation in large trade blocs (like EU/Schengen or ASEAN), and rigorous security standards that give other governments confidence when they stamp that stamp.

Just behind them, the United States, United Kingdom, Canada and Australia hover in the 150–170 range. Their passports remain formidable largely because of widespread bilateral visa-waiver programs: the U.S. Visa Waiver Program alone opens doors to 40 European and Asian states, while the UK’s Commonwealth connections smooth the way in parts of Africa and the Caribbean. Canada and Australia combine their own economic clout with selective agreements—Australia’s eTA for Canada and vice versa being one example—that boost mutual access without sacrificing border control.

On the other end of the spectrum, you’ll notice many developing-economy passports colored pale on our map. These lower rankings reflect a combination of limited diplomatic networks, concerns over overstays or economic migration, and, in some regions, lingering security risks. Small island nations and certain African and South Asian states often negotiate visa waivers last, since major powers prioritize reciprocity with strategic or high-volume partners.

Passport power isn’t static. In the last five years we’ve seen the United Arab Emirates climb more than 30 places after systematically signing new waiver agreements across Asia, Europe, and Latin America. Likewise, political crises can trigger sudden downgrades—as travel bans and suspensions ripple through reciprocal programs. For instance, Russia’s passport lost easy travel access to 15-20 countries since 2021 since the Ukraine war.

Welcoming Countries

“Vasudhaiva Kutumbakam” is a Sanskrit phrase meaning “the whole world is our home”. India, during its G20 presidency in 2022-23, used this as the motto for the G20 events. However, it is obvious that some families are more welcoming than others. If you have ever have applied for a United States visa from a developing country, you’d probably know what I’m talking about. When my parents applied for their U.S. tourist visa, it took them 1.5 years just to get an interview appointment at the consulate.

So, what countries are most welcoming? Asian countries are leading — Vietnam, Thailand and more.

When we render the Welcoming Score choropleth, one fact jumps out: it isn’t the world’s richest or most powerful states that lead on hospitality, but a cluster of sub-Saharan African nations. In 2025, nine countries admit every one of the 198 foreign passports visa-free or with visa-on-arrival! That list reads like a tour of West and Central Africa’s open-door pioneers: Togo, Equatorial Guinea, Côte d’Ivoire, Guinea, Comoros, Djibouti, Guinea-Bissau, Burundi and Nigeria. By eliminating practically all entry barriers, these governments have signaled that attracting visitors—whether tourists, investors or members of their diaspora—is a strategic priority.

Just below that “198-club” sits a second tier of African and a handful of island nations. Countries like Rwanda, Mozambique and Seychelles (each scoring 197–196) plus the Maldives and Samoa have likewise streamlined e-visa platforms or visa-on-arrival schemes to broaden access.

Contrast this with many Western and East Asian states, where high GDP per capita (PPP) and strong passports for their citizens don’t always translate into openness for inbound travelers. Europe’s Schengen Area and North America maintain tighter controls—often justified by security or immigration-management concerns—so their Welcoming Scores rarely breach the top 20.

In short, our map paints a clear picture: the most welcoming places in the world aren’t necessarily the wealthiest, but those that have made a conscious policy choice to throw their doors wide open. Africa and East Asia leads by example, proving that visa-free access can be a powerful catalyst for growth, goodwill and global connection.

Does Wealth Predict Passport Power?

To test whether richer countries really do have stronger passports, I ran two simple regressions of our Travel Easy and Welcoming scores on GDP per capita.

You can draw two clear, contrasting lessons from these regressions.

First, GDP per capita is a strong predictor of your Travel Easy Index: the coefficient of 0.00111 means that for every extra $1,000 in GDP per capita, a country can expect roughly one more visa-free or visa-on-arrival destination. The relationship is highly significant (\(p<2 \times 10^{-16}\)) and explains about 52 percent of the variation in passport power (\(R^2≈0.52\)). In plain English: wealthier countries tend to negotiate more visa waivers, but GDP only tells half the story—other factors like diplomatic ties, security partnerships and regional blocs fill in the rest.

By contrast, GDP per capita barely explains Welcoming Score. The slope is slightly negative (–0.000393), suggesting richer nations admit marginally fewer visitors without advance visas, but the effect is very small and only accounts for about 4 percent of the variation (\(R^2≈0.04\)). In other words, economic wealth doesn’t much predict how open a country is to incoming travelers. Some lower-income countries have adopted extremely liberal entry policies, and many wealthy ones maintain tighter controls.

Model	Term	Estimate	Std. Error	p-value
Travel Easy	(Intercept)	81.5109	3.1924	0.000
Travel Easy	GDP_Per_Capita	0.0011	0.0001	0.000
Welcoming Score	(Intercept)	126.2201	5.6594	0.000
Welcoming Score	GDP_Per_Capita	-0.0004	0.0001	0.006

R²	Model
0.52	Travel Easy
0.04	Welcoming Score

Conclusion

In a world where a simple booklet can open—or close—borders, passports embody far more than identity: they trace the arc of diplomacy, economic strategy and mutual trust. From the ornate UV-inks of New Zealand’s pages to the visa-free corridors enjoyed by Emiratis, we see how history and policy converge on paper. At the same time, the surprising generosity of many African and Asian states reminds us that openness is often a deliberate choice, not merely a by-product of wealth. As you plan your next trip, remember that behind every stamp lies a story of negotiation, goodwill and the promise of shared humanity. I definitely will.

What is my dissertation about?

Demand forecasting has a rich intellectual and practical history. Ancient texts like the Indian Arthashastra (350 BCE) and Chinese Han Dynasty archives both emphasized blending qualitative judgment with quantitative grain records to estimate demand. Fast forward to the industrial age, companies like Ford and Chrysler pioneered judgmental forecasting to support assembly lines. In the 1960s, statisticians like Box, Jenkins, Holt, and Winters developed foundational time-series methods like ARIMA and exponential smoothing, which still serve as industry baselines.

Yet these classical models have inherent limitations: they treat each time series in isolation, rely solely on historical demand, and often assume simplistic linear patterns. As demand environments became more volatile and complex—spanning thousands of SKUs across global markets—the need arose for scalable, data-driven approaches.

Machine learning (ML) entered as a powerful alternative. ML models can incorporate high-dimensional data, learn nonlinear patterns, and integrate external signals like marketing promotions or macroeconomic conditions. Most importantly, they enable a shift from siloed, local models to global forecasting systems that learn across products and markets.

Behind the Research: People Who Made It Possible

This dissertation—and everything it represents—would not have been possible without the kindness, intellect, and support of people across continents and stages of life.

First and foremost, my advisor, Dr. Chuanren (Charles) Liu, has been the intellectual anchor of this journey. His rare combination of sharp research instincts, generous time, and thoughtful critique shaped not only this dissertation but my growth as an independent researcher. He gave me remarkable freedom in defining my research path—a freedom I now recognize, in hindsight, as a true gift. I once discussed with Prof. Bobby how some advisors assign their own topics, making things easier in the short term but stifling long-term independence. That conversation only deepened my appreciation for Dr. Liu’s mentorship. I owe him more than I can ever express.

My internship and continued collaboration with HP have been central to this work. It wasn’t just a corporate stint—it became a living laboratory for my ideas. I’m grateful to Cara Curtland, Adam Ghozeil, and Jerry Hwang for their generous support in translating research into real-world impact. What made it special was HP’s willingness to treat this not as a mere “intern project,” but as a serious global initiative worthy of scale and rigor. That trust means a lot.

Dr. Sean Willems’ early mentorship gave me the mental scaffolding I still build on. His research remains a North Star, especially when I’ve felt adrift. His advice—often tucked inside thoughtful, incisive emails—has shaped my thinking in more ways than I can count. I’ve saved many of those emails, and I revisit them often.

I’ve been fortunate to build meaningful relationships with many professors at UT. Dr. Michael Galbreth, our department head, has a rare “yes-first” leadership style. His answer was always, “Let’s see how,” even when we asked for something as rare as a grad student pay raise. Dr. Wenjun Zhou has been a consistent source of encouragement—I hope we can collaborate on research in the future. Dr. Robert Mee offered guidance at critical junctures. Dr. Emre Demirkaya made “Statistical Learning” one of the most difficult—and rewarding—courses of my PhD, and also became a great friend. Terry Higgins and Charlie Cweik helped shape me into a better teacher, for which I’m truly thankful.

This path into research wouldn’t have begun without Dr. Pritam Ranjan, who nudged me early on at IIM Indore through summer internships and research papers. His belief in me during those formative years set everything else in motion.

Life in Knoxville would’ve felt a lot lonelier without the people who brought warmth and light. Nikhil Narayane has been a constant companion through shared road trips and memories. Yu Jiang has been a close and trusted friend, introducing me to Chinese culture (and hot pot!)—and I look forward to visiting China with her one day. Greeshma Geetha has a wonderful way of bursting my thought bubbles and grounding me in nature and environmental consciousness. Thanks to her, I notice the world more.

Pablo and I have had countless late-night debates on technology, programming languages, and the very fabric of the internet. To paraphrase Godwin’s Law—if most online conversations eventually devolve into references to Hitler, ours always loop back to the philosophy of tech. Samudra Dasgupta (and his dog Henley) brought color and chaos in the best way. Despite his quirks, Samudra is a kindred spirit, driven by the same idealistic goal—to make the world better than we found it.

A surprise gift of my time at HP was meeting Dea Bardhoshi. Her curiosity and presence have sparked many thoughtful conversations. Our weekly serendipity calls have helped keep my own curiosity alive.

And then there’s Meenal. My favorite person. Food for both my mind and heart. Her presence is an anchor, a mirror, and a source of joy. I find myself yearning for every next meeting with her.

Finally, to my parents—Rajendra Prasad and Chandra Lata Barnwal—my brother Shashank, and my sister Shalini: your unwavering love and patience have sustained me in more ways than you know. Everything I do is built upon your sacrifices and support. I carry you with me, always.

PhD in Pictures

Assorted pictures from the last four years.

The Heart of Good Sabzi

The beauty of Indian curry lies in its foundation — an aromatic base for vegetables to be fried into, and then turned into the curry. The vegetable (Sabzi) could be cauliflower (Gobi) resulting in Gobi Sabzi; eggplant/brinjal (Baigan Sabzi); mushrooms (Mushroom Sabzi); okra/ladyfingers (Bhindi Sabzi); or even a mixture of them (Mix Sabzi or Mix Veg).

Let’s start with what you’ll need. Don’t worry if the ingredient list seems long – most of these items can be found in your local grocery store, and the rest are worth a special trip to an Indian market. Trust me, your taste buds will thank you!

Choose Your Main Vegetable(s)

You can use zero, one or multiple vegetables. Each vegetable has its own taste. Using no vegetable would be Tamatar-Aloo Sabzi or (Tomato-Potato Curry).

• Cauliflower: 1 medium head, cut into florets
• Eggplant: 2 medium, cubed
• Mixed vegetables: 2-3 cups of your choice
• Mushrooms: 8-10 oz, quartered
• Bell peppers: 1-2, chopped

Instructions

Pro-Tips

1. Spice Adjustment:

   • Start with less spice; you can always add more. If you want to add more spices after adding water to the curry, you can do that in the Tadka (described below) or heating the spices first in some oil.
   • Taste frequently and adjust seasonings. You will get better with time.

2. Tadka (Final Flavor Boost):

   1. Heat 2 tablespoons ghee or oil in a small pan

   2. Add 2-3 dried red chilies

   3. Add 1 teaspoon cumin seeds

   4. Add 1/2 teaspoon red chili powder

   5. When spices sputter, pour over finished curry

Consistency in Curry Thickness

Different people have different preferences in the dryness of their curry. Some like dry curries (good for eating with bread) while others like watery curry (good with rice).

• For dry curry: Use minimal water and cook uncovered
• For gravy: Add more water and simmer covered
• Ideal consistency: Vegetables should be well-coated with thick gravy

Final Remarks and Troubleshooting Tips

As long as you follow the basic recipe, there is very less chance of getting something wrong. But remember, it is okay to make mistakes and its likely you will make mistakes. But those mistakes will teach you how to cook better.

The most important ingredient in cooking is time. Remember not to hurry or be too late. Some people hurry up in adding water before the veggies are well fried in spices. Some delay in stirring and the vegetable burns and sticks to the bottom. In that case, add some water and then stir instead of stirring dry.

What makes us happy?

One of the early realizations of my life was that happiness depends more on perspectives than circumstances. A wise person would strive for a perspective that brings them happiness. So, why isn’t everyone happy? To a large extent, it’s because we are told what should make us happy: job, marriage, kids, and so on.

But happiness isn’t just a momentary thing! Like bad experiences, sensations that bring happiness eventually change. Even if you get a nice job, a better one might make you slightly happier, but only for a short while.

Long-term studies have shown that lottery winners and individuals who lost a limb eventually revert to their previous “normal” levels of happiness.¹ Even other life events like marriages and child birth hardly affect happiness in the long term.

Money and Status

Sociocultural factors like status and role in society do have an impact on happiness. Some claim money brings happiness, and that’s true—but only to a certain extent. Someone earning $150,000 isn’t necessarily happier than someone earning $100,000.²

However, biologists insist that if happiness is measured as pleasure, it is determined by the chemical composition of balance of three biochemicals: oxytocin, dopamine, and serotonin.

If that’s the case, should people be drugged with the right amounts of these hormones? Thankfully, we’re saner than that—for the most part. Yet, this doesn’t stop us from doing things like putting VR headsets on cows to show them green pastures in farms. How cruel are we?³ Even if humanity achieves utopia, would it be utopia for the world? Most likely not.

Still, all this discussion revolves around pleasure. Happiness itself remains a mystery biologically. Someone with cancer could feel happy, while a perfectly healthy person might not.

How do we measure happiness?

What makes me happy?

We’ve established that representing happiness, both biologically and in survey design, remains elusive.

Therefore, I hypothesize: perspectives that make us happy require objective, unbiased, patient, and persistent observation. In other words, it requires observation of reality as it is, not as we would like it to be. A story from Buddha’s life illustrates this: On a cold winter night, Siddhartha Gautama, dressed in rags, was asked how he seemed so cheerful despite the harsh weather. Buddha replied that suffering does not come from the cold or the wind but from the mind. True contentment, he said, doesn’t depend on circumstances but on understanding the nature of the mind.

Essentially, happiness is a mental game. Humans often misplace their pursuit of happiness by chasing fleeting external stimuli—wealth, power, relationships—believing they bring lasting joy. Buddha’s teachings take a radically different view. The core idea of anicca (impermanence) is that everything in life—emotions, sensations, possessions, and even our identities—is transient. Suffering arises when we cling to these impermanent things. Vipassana (a special way to “see”) was Buddha’s method of teaching people to directly observe their sensations and see reality as it is.

Buddha also taught anapana (observation of respiration) as a “deliciously pleasant way of living.” So, what is happiness, if you ask me? It is the absence of suffering. If you’re not happy, you’re likely experiencing suffering. And what is peace? Happiness at rest. Happiness is closer to joy than pleasure.

Death, the fact that our entire life is impermanent, adds reasoning to happiness. Indeed, as Meenal says:

What does death teach us about being alive? That it is not permanent, and probably a punishment if it becomes permanent. The most comfortable life imaginable will become a prison for you once you have to live it forever. There are no ups without downs. It just becomes a plain never-ending vast surface.

Striving to know what makes me happy has always been important to me, maybe because my name Harsh (हर्ष) means happiness in Sanskrit/Hindi. Harshvardhan (हर्षवर्धन) means one who increases happiness.

Anyway, thanks for coming to my TED Talk. Maybe you’ll decide to find what makes you happy—or maybe not, but please do. Because more likely than not, it is different from everyone else in the world. In any case, I hope we’ve learned a thing or two about happiness.

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Some Fun Facts from World Happiness Survey

1. Younger generation (millennial and Gen Z) is more likely than their predecessors to help others in need, especially post-COVID.
2. Financial well-being (GDP per capita), Social support, Healthy life-expectancy, Freedom to make life-choices, generosity, and perception of corruption together can explain 78% of variation in life satisfaction (Cantril ladder score, Regression’s adjusted R2 = 0.78).
3. Older age is associated with higher life satisfaction in India, refuting some claims that the positive association between age and life satisfaction only exists in high-income nations. However, older women in India report lower life satisfaction than older men.

Additional Readings

1. How they find the “happiest” country on Earth, YouTube
2. Happiness and Life Satisfaction by Our World in Data
3. World Happiness Report, 2024