Positive-sum Games

Imagine you want to buy a cup of coffee on your way to work one morning. You are really craving for a fresh cup of coffee, but there’s obviously a limit to how much you are willing to pay to fulfill your desire. As a consumer, your best case scenario is to get a free cup of coffee. But assuming that free coffee is not available, you would like to pay as little as possible, and not a penny more than $2. This establishes the value of a cup of coffee for you.

On the other hand, a local coffee store owner would like to sell you a cup of coffee, and preferably charge as much as possible. Assuming that it costs $1 to produce a cup of coffee, the coffee store owner would not sell it for anything less than $1.

You go to this coffee store, and find out that a cup of coffee is priced at $1.50. You buy a cup of coffee thinking that it’s a good deal — 50 cents less than what you were willing to pay for it. In a sense, you made a profit of 50 cents in this transaction; 50 cents that you can use somewhere else. The coffee store owner also made a profit of 50 cents. Both parties tried to maximize their own profit, but as a result of this voluntary trade, both benefited.

Now there are other factors — like competition, scarcity, demand — that add complexity, but in its simplicity, this example demonstrates how in a free market, a trade between two parties will take place only when both parties benefit. Suppose there are no other coffee stores nearby, and the coffee store owner starts charging $5 for a cup of coffee. This will distance consumers like you away from them, and create an untapped market of consumers who are looking for cheaper coffee. If there are no artificial barriers to entrance (license requirements, etc.), new coffee stores will open quickly to capitalize on that segment of consumers.

This is a profound, but not widely understood, economic concept: when two parties voluntarily trade with each other in a free market they both benefit. Trade is a positive-sum game. Unlike a zero-sum game, like a robbery, where one party’s loss is other party’s gain, a positive sum game is a win-win for both parties.

A couple of years ago, Egde online magazine posed the following question: “What scientific concept would improve everybody’s cognitive toolkit?”, and Steven Pinker suggested the concept of positive-sum games. Also, check out this illuminating TED talk (linked below) in which Matt Ridley wonders how we became the only species that became more prosperous as we became more populous. And the answer, he argues, is exchange. He gives some interesting examples that demonstrate how exchange (trade) helps elevate living standards.

In the old days, if you were rich, you literally had people working for you. That’s how you got to be rich; you employed them. Louis XIV had a lot of people working for him. They made his silly outfits, and they did his silly hairstyles, or whatever. He had 498 people to prepare his dinner every night. But a modern tourist going around the palace of Versailles and looking at Louis XIV’s pictures, he has 498 people doing his dinner tonight too. They’re in bistros and cafes and restaurants and shops all over Paris, and they’re all ready to serve you at an hour’s notice with an excellent meal that’s probably got higher quality than Louis XIV even had. And that’s what we’ve done, because we’re all working for each other. We’re able to draw upon specialization and exchange to raise each other’s living standards.

Watch the whole thing, it’s quite fabulous.

Happy Pi Day 2013

From this year onwards, in addition to celebrating Pi Day on March 14th, I am going to celebrate Pi Approximation Day on July 22nd (22/7) as well. I can really use an additional day of celebration for my favorite mathematical constant!

By the way, here’s an interesting approximation of π: A nano-century is approximately π seconds long. In other words, if you divide the number of seconds in a century by one billion (nano = 1 billionth), you’ll get a result that’s close to π:

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The comic is from Dinosaur Comic.

Previous posts involving π: 3.14, A Sanskrit Mnemonic for π, Happy Pi Day!, A Mathematical Conundrum.

Buffalo buffalo

The following (unpunctuated) sentence seems nonsensical, but it is a grammatically valid sentence:

Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo.

Here’s how:

Survival Machines

Published in 1976, The Selfish Gene remains one of the most influential scientific books I’ve ever read. In this book, Richard Dawkins introduced the novel concept of the replicator: “the initial molecule that managed to reproduce itself and thus gained an advantage over other molecules within the primordial soup.” I was flipping through the first chapter of this book a few days ago, and the following passage gave me goosebumps all over again:

Four thousand million years on, what was to be the fate of the ancient replicators? They did not die out, for they are past masters of the survival arts. But do not look for them floating loose in the sea; they gave up that cavalier freedom long ago. Now they swarm in huge colonies, safe inside gigantic lumbering robots, sealed off from the outside world, communicating with it by torturous indirect routes, manipulating it by remote control. They are in you and me; they created us, body and mind; and their preservation is the ultimate rationale for our existence. They have come a long way, those replicators. Now they go by the name of genes, and we are their survival machines.

Take a moment to grasp the profundity of this rather unnerving passage. It begins to set-up the central premise of this iconic book, and its many-fold implications are unraveled with elegant prose and extensive detail.

Among other things, this excerpt alludes to the prevalence of behavioral traits that may not be beneficial to an organism (i.e., the vehicle) but still exist because they are favorable to the the genes (i.e., its drivers). The selfish genes do not “care” about their vehicle insofar as it can be used and manipulated for its own survival. Often, there’s no conflict between the long-term survival goals of the genes and and short-term survival motives of an organism. The gene’s longing for eternity is in accordance with an organism’s desire for a long life. But there are exceptions.

Consider the male spider, for instance. The sexual impulse of a male spider is beneficial to the “spider genes” because a potential copulation with a female spider increases their chances of surviving yet another generation. However, this often gets the male spider killed — by getting eaten by the female spider. Good for the spider genes, not so much for the poor male spider. Similarly, there are human traits and impulses that may be unfavorable to an individual, but are necessary for the survival of our selfish, manipulative genes. When I first read this book many years ago, this revelation blew my mind. It left an indelible impact on my understanding of evolution, and continues to shape my worldview even to this day.

The United States of Moon

Have you ever wondered how big the Moon would look if it were placed on the ground here on Earth? How much area do you think it would cover? Well, wonder no more. Here’s the US map projected on the surface of the Moon:

I agree with boreboarder8, who created this demonstration, that this does make the Moon appear much smaller than what I had imagined:

It was difficult for me to fathom the size of the moon, thus inspiring the creation of this map. For me, this map puts the scale of the moon much smaller than I previously imagined. But it’s really interesting hearing how others (already grasping the size of the moon) now see the US as larger.

Keep in mind that this is a rough estimation. It’s one thing to try to project spherical earth on a flat map, and another to project a spherical US map on another (smaller) sphere.

[Source: Reddit]

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Previous “Sense of Proportion” posts: I, II, III, IV, V, VI.

English Vinglish

There are myriad examples of articles and videos of people expressing their frustration with the discrepancy between the way English words are spelled and pronounced. If ‘to’ is pronounced as /to͞o/, and ‘do’ is pronounced as /do͞o/, then shouldn’t ‘go’ be pronounced as /go͞o/? If we don’t pronounce ‘p’ in ‘pneumonia’, why include it in its spelling? What’s letter ‘w’ doing in ‘answer’? The list is endless.

Well, lo and behold, here’s a 15-year plan to improve English spelling:

For example, in Year 1 that useless letter c would be dropped to be replased either by k or s, and likewise x would no longer be part of the alphabet. The only kase in which c would be retained would be the ch formation, which will be dealt with later.

Year 2 might reform w spelling, so that which and one would take the same konsonant, wile Year 3 might well abolish y replasing it with i and Iear 4 might fiks the g/j anomali wonse and for all. Jenerally, then, the improvement would kontinue iear bai iear with Iear 5 doing awai with useless double konsonants, and Iears 6-12 or so modifaiing vowlz and the rimeining voist and unvoist konsonants.

Bai Iear 15 or sou, it wud fainali bi posibl tu meik ius ov thi ridandant letez c, y and x — bai now jast a memori in the maindz ov ould doderez — tu riplais ch, sh, and th rispektivli. Fainali, xen, aafte sam 20 iers ov orxogrefkl riform, wi wud hev a lojikl, kohirnt speling in ius xrewawt xe Ingliy-spiking werld.

Hyperbole aside, I think this satirical passage does successfully wag a finger at the futility of imposing rules and restrictions on a language… of trying to “purify” it. Language is like an ever-flowing river. It has to keep evolving, and adapting. The fact that English has embraced words from many other languages is perhaps one of the main reasons why it is so successful. Yes, there are more exceptions than there are rules, it’s a bitch to spell, and is indeed a very phunny language (video link). But it’s here to stay. We must make our peace with it.

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PS: The above passage is attributed to Mark Twain.

PPS: This reminded me of an article written by Utpal Dutt regarding the supposed purification of Hindi language on Doordarshan TV back in the 80′s. I posted an excerpt here.

Two Prizes [Puzzle]

Suppose I offer you two prizes: prize A and prize B. You are to make a statement – any statement you like.

If the statement is clearly true, I will give you a prize. You will win either A or B, I am not saying which one.

And if your statement is false, you won’t get any prize.

It’s clear from this that you want to make a statement that is clearly true, because otherwise you won’t win any prize. You can say something like “One plus one equals two.” This is clearly true, and you will win either A or B.

However, let’s say you really would like to win prize A. The question is: what statement can you make that will ensure that you will win prize A?

[From Forever Undecided: A Puzzle Guide to Gödel]