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As π goes, so goes a circle

π is ubiquitous both in mathematics and physics. Its appearance in some contexts are intuitive to grasp. Others require intellectual contortion, a mind-bending that defies all intuition. Wherever π appears, a circle is always hiding, to be discovered irrespective of one’s intuition! Let us get started slicing π, and explore a few astonishing cases.

The Circle

History informs us that π had an elevated, almost divine status in ancient times due to beauty of the circle, its symmetry to which this ratio owes its origin. …

The Meandering Journey Of Photons

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In two previous posts, we saw the emergence of radicals naturally — with examples from Economics and Game Theory. In this third installment of the series, let’s see how they emerge in stochastic (or random) processes in nature. The star of this show is a photon — the emergence of low-entropy infra-red photons responsible for all life on planet earth.

We Didn’t Build That!

All organic life is carbon-based. The biochemical magic of a human body is the clockwork of a little over thirty-seven trillion cells, each with an infinity of carbon atoms. No lab has forged a single carbon atom yet. …

Voting Power: Packing A Punch

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Radicals pop up in unusual places. In a previous post, we saw how they emerge to maximize Utility. In this post, let’s explore Voting Power.

Voting Power

A cornerstone of a thriving democracy is the enfranchisement of its body politic. Qualified elected-representatives act on its behalf. In flexing voting power, citizens affect lasting changes to society. Its core idea is rooted in Game Theory and entails radicals!

The vote is the most powerful nonviolent tool we have — John Lewis

Power Vs Right

Voting power differs from voting right. The former measures the punch a single vote packs, whereas the latter determines if a vote…

Developing an Intuition for Radicals

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The word radical is overloaded in the vernacular probably because it is important. Catchy as the title may appear, our concern is math radicals! Pun aside, they are a mathematical construct — a product of the human mind. Their serendipitous emergence in natural laws is a curious fact. Is that coincidence?

It can’t be. Unlike the appearance of faces in clouds, they track reality and hold predictive power. They appear in diverse pursuits of inquiry such as Physics, Engineering, Economics, Game Theory, Biology, and Political Science. Is there a unifying theme that underlies their emergence?

In a series of posts…

Psychology of Animal Behavior: Part 3 of 4

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The Nature Of Knowledge

In fact, most of the ideas we have about the world and our civilization we have learned so that we are who we are in good measure because of what we have learned and what we remember — Eric R. Kandel, Dec 8, 2000


The universe is pregnant with knowledge. It got on without us for a very long time. Knowledge lay dormant in everything from quantum fluctuations to an atom, from DNA to a cell. Life tentatively flickered into existence in all its glorious forms powered by the free energy of our sun. In fits and starts and extinction…

Biological basis of Memory and Learning: Part 2 of 4

This is part two in the series. Part one is linked above. The scientific basis of human behavior as revealed by genomics and neuroscience is worth exploring.

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Many creatures share the web of life. We owe our existence to humble origins of an ancient common ancestor. It occupied a perch on the evolutionary tree long before our arrival. So do our cousins, the sea slugs, fruit flies, honey bees and other creatures. Sea slugs, the marine counterparts to snails, are interesting in particular.

What drives human behavior, nature or nurture?: Part 1 of 4

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This story is the convergence of two opposing lines of inquiry. One is introspective, gazing inward into the mind, and the other gazing outward into nature. Both lead to the discovery of a profound truth about animal behavior. I was inspired to write as I listened to this podcast.

  1. Nature’s crafting of animal behavior.
  2. Science catching up with Buddha’s original ideas.
  3. Breaking patterns detrimental to human well-being.

Gautama Buddha went against the grain of evolutionary animal behavior toward enlightenment by incisive introspection. Over two millennia later, Charles Darwin discovered evolution by natural selection and laid the scientific groundwork for animal…

What do Quasars, Corals, and Rocks have in common?

The question may seem odd. Many happy coincidences from seemingly unrelated fields have led to scientific breakthroughs in the recent past. They have helped solve puzzles that broaden our understanding of nature. One fascinating story involves quasars, deep-sea corals, and ancient rocks! First, it requires understanding long time-horizon phenomena unfolding in epistemic contrast to what humans can comprehend with our quirks, beliefs, and all.

Human Quirks

House of Mirrors at the Garden of Unearthly Delights: Photo Credits to Jesse Neill

Perception Is Not Reality

Objective reality is how the universe is. Perception is our subjective experience of it — how it seems. This distance separating perception and reality is a curious…

Last week, in a blog post titled Finding Patterns, I introduced a puzzle. I asked my teenager to solve it using only a pen/pencil and paper.

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?

Three Steps

Using a collaborative effort between human and machine, we can achieve more, while having fun solving problems and finding new patterns. Let’s try this in three steps. Step (I) is purely human effort. Step (II) is all brute power of the machine. Step (III) is a middle ground, a collaborative effort.

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Step I: Human Effort


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…

Dr. VK

Physicist | Poetic Naturalist | Philosophy, Science & Tech, Culture, Humanism, Mindfulness | @higgsmass

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