MATHEMATICS: eHow : How to build a math model in your spare time

Who are you?
You are a professional who would like to build a mathematical model in your spare time.

Why?
You have spare time, don't you? Yes, the time between arriving at the bus stop and getting on to the bus. And the time between getting to the train station and actually boarding the train. And also the time between getting to the shuttle stop and actually boarding the shuttle. Well, this is your opportunity to use your spare time for practical purposes. This post will outline how you can build a mathematical model in all that spare time that you have. This spare time would otherwise be used up making pointless Facebook posts. Well, now you have options. No, not stock options. You have to do actual work for that.

How?
This post is inspired by Hal Varian's remarkable paper "How to build an economic model in your spare time". Like the author of that paper, we believe that it is the simple lack of the availability of a post such as this one that has made it difficult for people to develop mathematical solutions to hard problems. Please note that, as is obvious, extensive research on mathematical work done in far-flung countries like Russia and Japan has been done as part of background reading for this post.

For those new to building mathematical models, this post will provide you some practical tips and expert guidance on the steps you can follow to build a math model - all in just your spare time. Which, after reading this little piece, you will have none left of. Because you will be so busy either solving mathematical problems - like Prof. Shankar - or resting on your laurels - like Prof. Manikutty - knowing that you don't have to do any more research. But remember that Prof. Manikutty knows that, in Japan, he is already a "prominent person". Prominent because he is the tallest person around for miles and miles.

n-ary oppositions

I am coining a new term in the field of deconstructionism and in the field of Western philosophical thought. It is the term "n-ary opposition". It is, I believe, a new concept for Western philosophy. Below is an explanation of n-ary opposition. To be honest, it is a bit of a cut-and-paste of the Wikipedia entry for "binary opposition". But I am perfectly serious about all of this.

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N-ary opposition


In critical theory, an n-ary opposition (also n-ary system) is a set of n related terms or concepts which are spread over a 'spectrum' of meaning. The term, introduced by the columnist Anand Manikutty, is also used to refer to the opposition that exists among the n concepts. Binary and ternary oppositions are common types of n-ary oppositions. A binary opposition is a set of two related terms or concepts which are opposite in meaning. A ternary opposition is a set of three related terms or concepts. A ternary opposition may be a set of three related terms of concepts out of which two are opposite in meaning and the third is a null concept. Ternary opposition, also a term introduced by Anand Manikutty, is the system by which, in language and thought, three theoretical opposites are strictly defined and set off agsinst one another. It is the contrast between three mutually exclusive terms, such as positive, negative and zero. Another example : up, down and "middle" (although various other terms may be used in place of "middle" such as zero position). A third example is left, right and "middle". Again, various other terms may be used in place of "middle".

N-ary opposition is proposed as an important concept within structuralism which sees such distinctions as fundamental to all language and thought. In this extension of structuralism, a n-ary opposition is seen as a fundamental organizer of human philosophy, culture and language.

Comment : comment to Prof. Sieg Hecker

Here are some comments I sent to Prof. Sieg Hecker, a world expert on nuclear weapons.

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In the case of India, I have been surprised that India continues to adopt what I would term an 'underdog' stance. India talks about nuclear 'have's and 'have-not's and justifies its own nuclear own program on this basis. I believe this to be a mistake. I think it would be better for India to adopt a policy of 'persistent ambiguity' (or, if you prefer, 'calculated ambiguity'). 

Go First dice

From 'The Guardian' :

When two or more people roll a die each in order to see who scores highest – what you do, for example, when deciding who goes first in a board game – there is always the chance of a tie. In the event of a tie, of course, you roll again. But then there is still the chance of a tie. And this can go on ad infinitum. 

In other words, the process is not as efficient as it could be. Eric wondered if he could come up with a set of fair dice such that one roll of each die is enough to establish an absolute winner. In devising a solution – and thus saving the board game players of the world hours and hours of lost time – Eric and a friend have made the greatest innovation in dice technology in recent years. 

Their set of four "Go First" dice (pictured above) are such that when two, three or all four of the dice are rolled together: 

1) no ties are possible.2) each die has an equal chance of displaying the highest number. 

Eric's friend is Robert Ford, a mathematics professor at Dalton State College, Georgia. Initially they were considering a set of eight cubic dice, but Robert worked out that it was impossible to have a set of cubic dice that satisfied the two conditions. He then looked at a set of four dodecahedral dice – the 12-sided dice that are used in Dungeons & Dragons – and after a week found a solution, which include all the numbers from 1 to 48 with no repeats: 

Die 1: 1, 8, 11, 14, 19, 22, 27, 30, 35, 38, 41, 48 

Die 2: 2, 7, 10, 15, 18, 23, 26, 31, 34, 39, 42, 47 

Die 3: 3, 6, 12, 13, 17, 24, 25, 32, 36, 37, 43, 46 

Die 4: 4, 5, 9, 16, 20, 21, 28, 29, 33, 40, 44, 45 

These dice satisfy Eric's requirements: if you roll any subset of them, each die has an equal chance of winning.

India and Olympic sports

It has been an increasingly common complaint that Social Scientific Theories lack predictive power, but the ones I discuss below do not suffer from this problem. I can confidently state that for every year that is divisible by four, India will send a contingent to the Olympics and that said contingent will perform underwhelmingly. Furthermore, I can also quite confidently assert that there will be a general outpouring of strum und drang following each Olympics in India where journalists and everyday folks like you and me wonder if there is something we are doing wrong. Nirmal Sekhar writes about the performance of India in the most recent Olympics in The Hindu :

My dear readers, let us get real. We have failed the Koms and the Yogeshwars and the rest as much as we seem to believe that many Indian athletes have failed us. They don’t owe us as much as we owe them.

We need to follow their careers, cheer them from grassroots up, care about how they are treated by the administrators, worry about how they are ignored by the big corporate giants who would readily part with $10m for a 15-second TV ad campaign featuring a Sachin Tendulkar or a Gautam Gambhir. But we don’t.

We simply don’t give a damn most of the time and then bemoan their lack of success at the Olympics once every four years.

Other transliteration schemes

Three other transliteration schemes are the ITRANS scheme, IAST and Velthuis. Here is what the Devanagari vowels look like in these above schemes (table courtesy Wikipedia).

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Vowels

Devanāgarī	IAST	Harvard-Kyoto	ITRANS	Velthuis
अ	a	a	a	a
आ	ā	A	A/aa	aa
इ	i	i	i	i
ई	ī	I	I/ii	ii
उ	u	u	u	u
ऊ	ū	U	U/uu	uu
ए	e	e	e	e
ऐ	ai	ai	ai	ai
ओ	o	o	o	o
औ	au	au	au	au
ऋ	ṛ	R	RRi/R^i	.r
ॠ	ṝ	RR	RRI/R^I	.rr
ऌ	ḷ	lR	LLi/L^i	.l
ॡ	ḹ	lRR	LLI/L^I	.ll
अं	ṃ	M	M/.n/.m	.m
अः	ḥ	H	H	.h
अँ			.N

The world's largest known prime - and a puzzle

Courtesy Fabrice Bellard, here is a compact computer program in C to print out the world's largest known prime.

int m=167772161,N=1,t[1<<25]={2},a,*p,i,e=34893349,s,c,U=1;g(d,h){for(i=s;i<1<<24;i*=2)d=d*1LL*d%m;for(p=t;p<t+N;p+=s)for(i=s,c=1;i;i--)a=p[s]*(h?c:1LL)%m,p[s]=(m+*p-a)*(h?1LL:c)%m,a+=*p,*p++=a%m,c=c*1LL*d%m;}main(){while(e/=2){N*=2;U=U*1LL*(m+1)/2%m;for(s=N;s/=2;)g(17,0);for(p=t;p<t+N;p++)*p=*p*1LL**p%m*U%m;for(s=1;s<N;s*=2)g(29606852,1);for(a=0,p=t;p<t+N;)a+=*p<<(e&1),*p++=a%10,a/=10;}while(!*--p);for(t[0]--;p>=t;)putchar(48+*p--);}

The program is just 438 characters in length. It compiles quite quickly on the MacBook Pro and requires less than 5 minutes of running time.

This number, the largest known prime, belongs to a class of primes called Mersenne primes and has the value  2^43112609-1. It has no less than 13 million digits. I ran the program earlier today, and have pasted the first ten lines or so of the output below. I have a little mnemonic scheme to remember long strings of numbers and so I created a mnemonic to remember the first ten digits of the number. And so if you ever wanted to commit to memory the digits of the world's largest prime, you can start right here :

Harvard-Kyoto : a very brief note

A follow up to my post on the Tamil writing system. Some people had asked what the Harvard-Kyoto system referenced in the original post was and so, a few words on Harvard-Kyoto.

Harvard-Kyoto is a transliteration scheme for Devanagari. I am making a conscious attempt to keep the learning curve for this system as short as possible, and so, in that spirit, a very brief summary of Harvard-Kyoto is given below.

   a A i I u U R RR lR lRR e ai o au M H
   k kh g gh G c ch j jh J
   T Th D Dh N t th d dh n
   p ph b bh m y r l v z S s h

Anybody who has learnt Hindi would know what I am referring to here. These are the basic Devanagari vowels and consonants written out in ASCII. You can also refer to the Wikipedia entry on Harvard-Kyoto which is available here. That is more or less all the introduction you need to understand Harvard-Kyoto.

Comment : Email to Schelling on employees having to be "on" all the time

Below is an excerpt from my email to Nobelist Thomas Schelling on an issue that is increasingly affecting a lot of employees around the world, not the least back office workers in India.

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It seems that the concept of credible commitment has applicability to the "being on" problem within organizations. Organization behaviorists have been concerned for a while now about the increasing demands on employees to be *on* - on email, on Blackberries, on call - and not just on during work hours, but on all the time.

"Being on" for an employee implies greater costs (exertion, et cetera) borne by employees. It is unclear that there is always a significant benefit arising out "being on" outside of work hours. The benefit to the employee or the company may be marginal. In many cases, it may, in fact, be more efficient for an employee to deal with all of her email in one shot than to break up her work-day by frequently checking email because these interruptions may require the employee to stop work on whatever it is she (or he) may be working on. The breaking up of the work-day may take a physical as well as psychological toll on employees - people want to help others, but first, they want to just get their own jobs done. Furthermore, in many cases, there is nothing happening outside of work hours that requires the employees to "be on" in the first place.

This may be modelled using the Prisoner's Dilemma matrix. Assume that we have two players. If both players checked email only during work hours, then both of them would benefit. If one of them defected and decided to check email all the time, he would be perceived as a good employee, and the other employee would get the Sucker's Payoff, which would be lower than if they both cooperated. That means that the only Nash Equilibrium is where both players defect.

It is, however, in the interest of the organization as a whole for employees to be satisfied, and so it might make sense for companies or units within companies to set limits on when employees are required to be on. Today, more and more employees are complaning that they are being overloaded with work. They feel tired. They feel overwhelmed. But more work hours does not equal more work done. If organizations made a credible commitment to employees, say, by installing software on the devices of the employees, so that they would not have to "be on" unless required, then employees may not feel it nescessary to analyze for equilibria.  It seems that by encouraging employees to Cooperate at the organizational or sub-organizational level, one may realize more productive - and happier - employees.

==

A breakthrough result in cryptography

Stanford's Craig Gentry's paper on the first ever fully homomorphic encryption scheme has been picked up recently by a mainstream publication. At least, insofar as the American Scientist qualifies. An article by Brian Hayes (thanks, Three Quarks Daily!):

Alice hands bob a locked suitcase and asks him to count the money inside. “Sure,” Bob says. “Give me the key.” Alice shakes her head; she has known Bob for many years, but she’s just not a trusting person. Bob lifts the suitcase to judge its weight, rocks it back and forth and listens as the contents shift inside; but all this reveals very little. “It can’t be done,” he says. “I can’t count what I can’t see.”
Alice and Bob, fondly known as the first couple of cryptography, are really more interested in computational suitcases than physical ones. Suppose Alice gives Bob a securely encrypted computer file and asks him to sum a list of numbers she has put inside. Without the decryption key, this task also seems impossible. The encrypted file is just as opaque and impenetrable as the locked suitcase. “Can’t be done,” Bob concludes again.
But Bob is wrong. Because Alice has chosen a very special encryption scheme, Bob can carry out her request. He can compute with data he can’t inspect. The numbers in the file remain encrypted at all times, so Bob cannot learn anything about them. Nevertheless, he can run computer programs on the encrypted data, performing operations such as summation. The output of the programs is also encrypted; Bob can’t read it. But when he gives the results back to Alice, she can extract the answer with her decryption key.
The technique that makes this magic trick possible is called fully homomorphic encryption, or FHE. It’s not exactly a new idea, but for many years it was viewed as a fantasy that would never come true. That changed in 2009, with a breakthrough discovery by Craig Gentry, who was then a graduate student at Stanford University.  

Here is a link to the incredible result first published in STOC. This is, of course, an absolutely breakthrough result and it has led to a number of subsequent papers which have extended the concept in many ways. There has been a number of subsequent papers on this topic by another rising star, Vinod Vaikuntanathan, who has this to say on a first application of the system.

When I asked Vaikuntanathan what application he thought might be deployed first, he had another suggestion: spam filtering. If you publish a public key and invite correspondents to send you encrypted email, a spammer can take advantage of the key to encrypt advertisements and the other effluvia that fills our mailboxes. Spam-filtering services cannot read and reject the encrypted spam unless you are willing to share your decryption key; homomorphic encryption could solve that problem.

Computer science tackles a 30 year old economics problem

From MIT news:

In 2007, the University of Chicago's Roger Myerson won the Nobel Memorial Prize in Economic Sciences — in part for research he had published, in 1981, on auction design. Using the tools of game theory, Myerson showed how to structure an auction for a single item such that if all the bidders adopted the bidding strategies in their best interest, the auctioneer would realize the greatest profit.

Myerson's work immediately raised a related question: What's the best way to organize an auction in which bidders are competing for multiple items? That question has stood for 30 years, but MIT computer scientists believe that they have now answered it. In a pair of recent papers, Constantinos Daskalakis, the X-Window Consortium Assistant Professor of Computer Science and Engineering at MIT, and his students Yang Cai and Matthew Weinberg describe an algorithm for finding an almost-perfect approximation of the optimal design of a multi-item auction. 

The manifest destiny of artificial intelligence

From the Scientific American :

Artificial intelligence began with an ambitious research agenda: To endow machines with some of the traits we value most highly in ourselves—the faculty of reason, skill in solving problems, creativity, the capacity to learn from experience. Early results were promising. Computers were programmed to play checkers and chess, to prove theorems in geometry, to solve analogy puzzles from IQ tests, to recognize letters of the alphabet. Marvin Minsky, one of the pioneers, declared in 1961: “We are on the threshold of an era that will be strongly influenced, and quite possibly dominated, by intelligent problem-solving machines.”

Fifty years later, problem-solving machines are a familiar presence in daily life. Computer programs suggest the best route through cross-town traffic, recommend movies you might like to see, recognize faces in photographs, transcribe your voicemail messages and translate documents from one language to another. As for checkers and chess, computers are not merely good players; they are unbeatable. Even on the television quiz show Jeopardy, the best human contestants were trounced by a computer.
In spite of these achievements, the status of artificial intelligence remains unsettled. We have many clever gadgets, but it’s not at all clear they add up to a “thinking machine.” Their methods and inner mechanisms seem nothing like human mental processes.

Perhaps we should not be bragging about how smart our machines have become; rather, we should marvel at how much those machines accomplish without any genuine intelligence.

The Tamil writing system as an app - a response to some comments

At least a couple of people raised the concern regarding whether the Tamil writing system proposal would require people to learn new sounds. It seems that the concern is about the audience for the writing system - - or as I would like to put it, the concern is regarding the market and any potential requirements placed by this product on the market's population. It would be useful to clarify at this point that the target market for this is people in the United States and Singapore. Furthermore, it is only for specialized users. It is only for people who would want to represent these sounds. It is not intended for elementary and middle school children, for example. Again, I would like to emphasize that this system is only intended for use by specialized users.

The reason for my choosing this population is not that this system would only work for specialized users from the United States and Singapore. The reason is that, first, this subject area is highly political and so I want to basically avoid all the politics around this by simply saying that this system is being made available for those who would like to use it. If you don't like it, don't use it. As simple as that. This also allows me to not worry too much about politics involving people in the Third World, academics in various departments in various universities, et cetera. These people may not have had the best educational opportunities and may therefore have trouble learning entirely new sounds (because they may be from extremely disadvantaged backgrounds). I am referring, of course, to the people in the Third World, the first population referenced. The question of whether this former population of people should be made to learn new sounds and letters arises (given that the educational system in the Third World is uneven in terms of quality) and this is certainly a valid concern. Second, there are many sociological concerns about whether new sounds should be introduced into a language in the first place. However, as I clarify below, I am not proposing to introduce any new sounds into Tamil. This system is intended simply to represent sounds that journalists and writers in Tamil already are required today to represent as part of their jobs.

Indeed, I have kept my system to what  I would like to call an optimal minimum - neither so little is proposed that no significant value is attained nor so much that it creates political problems. When I think back to some results I have seen in the field (based on some work I was doing while at Harvard Business School), it would appear that it would be better for languages to have fewer symbols and sounds, not more, especially since having a very large number of symbols and sounds may impose a heavier burden on poorer children (and note that I am talking about poor children in the Third World) who may already know to speak the language (as native speakers) but do not have family members who can teach them to read. This is indeed a good reason why policy makers would not want to allow new sounds in a language. In fact, I think that this may be the only one good reason why issues around language would acquire a political hue. It is for this reason that I am not proposing to introduce any new sounds into Tamil.

Conway's "Game of Life"

Where is the Java? Trust me - it is coming. First, look what I found! A cool simulation of Conway's "Game of Life" on Youtube :


What is the Game of Life? If you don't already know what the Game of Life is, it is a sort of artificial simulation of life. It basically works exactly as the video above shows. A set of rules is specified in a square grid consisting of cells and based on these rules, the game evolves. It is a game in the sense that it is similar to the sorts of games (such as "Go" and "checkers") that you and I might play but it requires no players at all. Once you set up the initial configuration, the 'game' plays itself. The Game of Life was devised by the mathematician John Conway, and the rules of the game are the following three simple ones:

1. A dead cell with exactly three live neighbors becomes a live cell (birth).
2. A live cell with two or three live neighbors stays alive (survival).
3. In all other cases, a cell dies or remains dead (overcrowding or loneliness). 

As the video says, the Game of Life is a simple illustration of 'emergence', that is, the idea that the application of a few simple rules can generate complex systems. A Java applet simulation of the Game of Life is available here. It is quite fun to play around with this thing. You can start out with some of the patterns they have on the webpage and press "Go" on the applet to see how things evolve from there. You can create a number of complex patterns starting with very simple ones. Check it out if you get the chance.

A modest proposal towards modernizing the Tamil writing system

It is June, but May and the theme of language and Talk were not so long ago. Given that, I will post on this here blog a modest proposal that goes towards modernizing the Tamil writing system. This post was occasioned by a comment on a Quizzing forum from earlier today. I have been meaning to talk about this for a while, but never got the chance to do so on my blog or my List.

The point came up on the forum that there is a rule in Tamil against using consonant clusters (like 'Tm'). This was brought up in the context of a controversy around the naming of a road in Tamil Nadu (the 'Mahatma Gandhi Road'). The controversy was around - get this - the use of the word 'mahATma' for a road in Tamil Nadu. The problem apparently is that 'mahATma' is a word that is of Sanskrit origin. Now, Tamil Nadu happens to be a state that is very proud of its language, but at the same time, there is a great deal of politicking on linguistic identity going on out there, especially during election time. All that posturing and politicking over linguistic identity seems utterly pointless, and it is really little more than a cynical ploy on the part of the politicians. However, the threat to Tamil from Hindi seems to be an always popular theme among voters in Tamil Nadu, and this bit of linguistic populism still has popular support. So what is to be done?

I would like to suggest the following : let us modernize the Tamil language to the greatest extent possible. Many of the rules currently governing Tamil come from premodern rules of language. This includes rules from Middle Tamil, et cetera. The solution is simple : copy Hindi. Do whatever Hindi does in terms of the writing system in Tamil as well. This would allow adopting words from Hindi and other Indian languages without change in Tamil. My proposal below includes allowing for aspirated consonants, for consonant clusters, and for better distinguishing of what I like to call the 'soft' consonants (as distinguished from the 'hard' ones.) My proposal would involve the following three simple changes to the Tamil writing system :

1. Consonant clusters: The proposal here is simple : allow for all consonant clusters. Mix and match as you please. Basically, allow the 'sTrI's, the 'zrIs' and the 'sprees'.

2. The soft consonants ('ga' versus 'ka', 'ja' versus 'cha', et cetera): there is a total of 20 consonants (velar, palatal, retroflex, dental and labial) in the primary table in DevanAgari (see table linked here). Tamil could simply use the same set of sounds in its writing system. It does so in any case in practice. It would be relatively simple to introduce a new mark to distinguish the first consonant from the third consonant in each category (velar, palatal, retroflex, dental and labial) (noting that the second and the fourth consonants are aspirated sounds). One could add the horizontal bar on top of the symbol for the third consonant in each category to distinguish that one from the first. This would be a way of acknowledging the role of Sanskrit (and Panini) in the development of this writing system.

3. Aspirated consonants: The proposal here is pretty simple again : allow for aspirated consonants. Aspirated consonants are ones for which you expel a extra bit of puff of air as you pronounce them. (Anyone who knows Hindi can tell you what the aspirated consonants in Hindi are.) I am talking, of course, about the 'kha' consonant (as opposed to the 'ka' consonant), the 'gha' consonant (as opposed to the 'ga' consonant), et cetera. The writing system could easily accomodate this using some symbol to distinguish the aspirated consonants. I would suggest for us to use the 'therefore' symbol (already used in Tamil to distinguish 'fa' from 'pa') following the letter to distinguish aspirated consonants from non-aspirated ones.

Using (2) and (3), you would end up with the same set of consonants as Hindi/Sanskrit. This would make communication using Tamil much, much easier. As regards (1), this requires no changes to the language at all. Even simply allowing all consonant clusters would greatly simplify matters and enable in modernizing the Tamil language. Wikipedia indicates that this process is underway in any case : "Contact with European languages also affected both written and spoken Tamil. Changes in written Tamil include the use of European-style punctuation and the use of consonant clusters that were not permitted in Middle Tamil" but it would be good to take it to a logical/rationalistic conclusion. As I mentioned at the forum, I went through Harold Schiffman's book on Tamil grammar at one point of time. It was an interesting book to read. At the same time, it is not very understandable for the naive user of the Tamil language. This grammar stuff does not have to be complicated. I only wish they modernize the Tamil writing system sooner rather than later.

Note that I have followed the Harvard-Kyoto convention throughout in this post for all italicized words (not that you need to know this to see where I am going with this proposal). Indeed, you could simply use the Harvard-Kyoto system for writing in Tamil and avoid all the problems I mentioned above. Many people use this in any case.

I have ensured that the suggestions in this proposal are as simple as possible to keep things constructive. If you had any comments on this, I would love to hear them. Please feel free to email me at the same email address as before. Enjoy!

Update (July 7th): In order to make things easier for Unicode users, I would like to add that the proposal includes using the Unicode symbol 0955 (which is unmistakably different from any other symbol yet similar to the horizontal bar in Hindi/Sanskrit) as an alternate way to add the horizontal bar for Tamil characters. Furthermore, preferably, the Unicode symbol 0955 ought to be placed on top of the 'therefore' symbol to indicate that this symbol is being used to indicate aspirated consonants. Please see the attached Unicode charts to see what symbols it is that I am referring to in this post. The symbols in question are Unicode characters 0955 and 0B83.

Panini, de Saussure, Chomsky et cetera

A followup on the "Pizza and Panini" piece. The "Pizza and Panini" piece is a sly comment on the Eurocentricity of the way we view contributions to science by the ancient Greeks versus the ancient Indians. Panini was, in my opinion, one of the greatest innovators in the ancient world. His grammar was the world's first formal system of language. Panini's ideas of formal rules in natural languages, in fact, significantly influenced the 19th and 20th century linguists who came after him - de Saussure's work (de Saussure,1894) and Chomsky's (Chomsky, 1957).

I am also poking a bit of fun at the lengthiness of some of the works of the ancient Greek mathematicians, scientists and even philosophers. Many of their dialogues appear unnecessary lengthy when viewed by us today. This is because the ancient Greeks had not yet developed the theories of languages, physics, et cetera that were developed after the European Enlightenment. If Euclid's propositions were analyzed today, we would find that they could have been written far more compactly. Two examples follow. The stuff in italics is all that would have been required for a Proof or Algorithm for the two Propositions of Euclid that I deal with below.

Origami, office hours, et cetera

So I did a practice run of the "Why are there cows on the street in India?" talk, and we have a video recording of the talk available. After the talk, I sent Prof. Tom Kosnik a letter about the video with some explanatory comments. The letter is linked here. Prof. Kosnik is, of course, familiar with the Case Method of lecturing. I just added enough detail about the Case Method, et cetera, to my letter so that it would be generally useful if I forwarded the letter on. Readers, one thing : please take a look at my previous post on this topic (linked here) and let me know if there is anything that needs clarification. The post is supposed to be self-contained and self-explanatory, and if it is not, I would be interested to know how I can improve it. Also, I will be holding office hours Monday morning (May 21) between 8:00 and 9:00 a.m. PST.

And in the meantime, to keep those little grey cells working, here is an interesting talk by Robert Lang who merges mathematics and engineering principles in ... oh, you just have to watch.

 

Pizza and Panini

Indiatimes' main page is carrying an edited version of the latest installment of our mathematics column entitled "Pizza and Panini". It is written in the style of the New Yorker. Hope you enjoyed reading it as much as we enjoyed writing it. (For those who came in late, Chandrayaan-12 is the rocket on which Anand and Ravi are traveling.) Please send in your answers to the puzzle in the column to the following email address : askthedelphicoracle@gmail.com. Happy solving!

PIZZA AND PANINI

This article is in collaboration with Prof. Krishnan Shankar, Professor of Mathematics at the University of Oklahoma.

The Oracle Asks

The Sanskrit grammarian Panini is at his friend Socrates’ place in Athens.

-+- 

Boy. Here is the tea.

Socrates. Thank you.

Panini. The boy, he understands Greek Mathematics, does he not?



Socrates. Yes, indeed; he was born in the house.



Panini. Can you talk to him about mathematics?

Soc. Certainly. Attend now to the questions which I ask him, and observe whether he learns of me or only remembers.

 

Cows in India, or What Gets Measured Gets Managed

Prefatory Note: This is intended to be a talk, not an article. Please treat it as a sort of transcript of my talk. In particular, expect low information density. I find that much of the information in TED-style talks comes in the Q&A. My lecture is really in a very different tradition, if you will, of lecture, namely, the Case Based method of teaching. The aim of the lecture is to inform the audience assuming that they have already read the Case Materials beforehand. It is a more intimate setting, but makes for a much richer experience. Furthermore, with the Case Method and unlike in a regular talk, you can engage with nearly all the members of the audience on substantive issues related to the topic at hand during the course of the lecture itself. Thus, the Case Method technique serves as validation for the idea itself. Using this technique, I have given this speech a few times thus far, and have found the main idea validated each time. I hope you enjoy the presentation.

The Talk:
I created and uploaded a video of my talk for my meeting with Prof. Lietz, but unfortunately, my Macbook has a soundcard problem, and so the sound is simply not showing up. Here is the video.



The title of the talk is "Why are there cows on the road in India?" In this post, I will provide a brief walkthrough of the talk since there is no sound. This is meant to be a very accessible talk so please feel free to write in if there are any questions at all, but please do bear in mind that this is a talk and so it is meant to be heard, not read.

My basic argument is simple. The way Indian Assemblies work today is dysfunctional, and we need a system of checks and balances there. There is just too much commotion in the Indian Parliament and State Assemblies today. (I have a clip from one of the State Assemblies in my video above (6:12 to 6:28). You will see footage here of an incident involving two members that occurred in the Kashmir State Assembly.) Things are clearly not working. I propose that we need to have a system of checks and balances in Assemblies and in the Parliament to make sure order is restored. I propose one such system (Proposal A - please see below), but it does not necessarily have to be the one that is adopted. In fact, even if the Parliament does not adopt this proposal, people could use a variant of the proposed system to keep tabs on the politicians themselves (Proposal B - also see below). What gets measured gets managed. What these proposals offer is a way for people to measure the performance of the members of parliament (MPs). If people can keep track of the performance of their members of parliament, they could put pressure on the politicians to do something about it.

Pizza and Panini

The third installment of our column is coming up at the Times of India. And to give you an update on the TEDx talk - my preparations for the TEDx talk are coming along well. Tomorrow, I am scheduled to talk to Nori Gerardo Lietz, an expert on world real estate markets here at Stanford. So exciting!

I expect to have an interesting talk with her and I imagine she would have some very interesting things to say on the topic, which <drumroll> is "Why there are cows on the street in India?" Anyway, the latest installment of our column is almost there. Hope you enjoy this month's puzzle.