The Importance of Having Friends Who Disagree

Paul Graham says, in one of his essays (emphasis mine) "....Why do you need other people? Can't you just think of new ideas yourself? The empirical answer is: no. Even Einstein needed people to bounce ideas off. Ideas get developed in the process of explaining them to the right kind of person. You need that resistance, just as a carver needs the resistance of the wood.

This is one reason Y Combinator has a rule against investing in startups with only one founder. Practically every successful company has at least two. And because startup founders work under great pressure, it's critical they be friends....."

In my experience, this need for "friendly resistance" extends to far more than creating startups. Every time you have a new idea, you need people you can bounce it off. To get any real benefit out of this process you need people with a complex combination of characteristics.

They should

1. have firm (but not rigid) opinions on their own
2. have logical reasons for those beliefs and be able to articulate them clearly
3. are driven by ideas and not ideology
4. not attach their egos to their opinions.
5. be willing to concede a valid argument even if it forces them to possibly re-examine their beliefs
6. know how to listen

Given all that, it is extremely difficult to find such "friends who disagree". I have been fortunate to have quite a few people around me, who have major disagreements with me, but are still friends (e.g see the discussion I had with KD in the comments section of my last blog entry).

Many people make the mistake of sorrounding themselves with people who think exactly like them and reinforce every idea or prejudice they have. This is a bad mistake and will often end up distorting the reality you see. One needs the corrective bucket of cold water in one's face once every so often. The only problem with surrounding yourself with bright people who think differently is that you may occasionally find that one of your ideas isn't as hot as you think it was or that one of your deeply held convictions is just plain wrong. This is dificult for some people because they make the rightness of their ideas a validation of their worth as persons. Blogging is a great way to expand this circle. But it can work both ways and one may end up with a "fan club" that just reinforces your prejudices.

So do a quick test right now. Make a list of your closest friends/acquintances/advisors. Then make a separate list of those who think totally differently from you, but are worth listening to anyway. Look at the intersection of these lists.

You may be surprised.

Yet Another Math Milestone

A few days ago, I discovered an error in the mathematics of a paper (on neural network optimization) being prepared for publication by a very eminent scientist. My drawing attention to this discrepancy in the proof has led to a total recasting of the approach to the problem and I will be now listed as a co-author of the paper.

Hmm yeah. Whatever. So how is this significant?

Well this is the first time I have used my skill in mathematics (vs my skill in programming) to contribute significantly to a scientific effort. In an old blog post I had theorised that the acquisition of "mathematical thinking" would follow a four step path. I said ..

1. the first step in mastering math is be to learn to read the notation. just like learning the syntax of a new programming language
2. the second is to grasp the reality expressed by the notation at a gut level , like understanding the paradigm and patterns lying underneath a programming language , like ,say ,beginning to grok "oo"
3. the third is to use that understanding to create new possibilities
4. the fourth is to use a programming language to embody and refine those possibilities , thus creating programs that do what has never been done before.

On this scale, after more than a year of very hard work, I seem to be half way through the third step. I am now able to "think in math" just as (good) programmers are able to "think in objects"(or functions, or whatever the underlying abstraction of the language is) to a point where I can examine the line of a mathematical algorithm and extrapolate it in into new directions to limited distances. As of today I am not able to think "freewheelingly" in math and my ability to think programatically far outstrips my ability to think mathematically, but these two modes of thinking seem to be duals of each other.

Programmatic thinking somehow seems to investigate the "structure" (and the structural integrity) of a solution to a problem while mathematical thinking focusses on the abstract essence of a problem and the "degree of rightness" of a solution.

One is not a substitute for other. Thus I am very doubtful that "merciless refactoring", for example, gives any real insight into the nature of a problem, like many "agilists" claim. At best it gives an insight into the structure of a proposed solution. This grants only an indirect perspective onto the problem space. I have seen many excellent programmers who were relentless practitioners of "agile" work in a domain (say retailing) for years and still not really understand the "essential nature" of the domain (vs creating good solution structures). In other words they function like draftsmen with no artistic spark, repeating the same patterns endlessly without any genuine understanding or insight. Frequent "domain hopping" , whereby you work on a retail project for a few months, then move to "banking" then to "insurance" and so on, helps to deepen this focus on purely programmatic skills till every project becomes a blur of "billable hours" and "database->gui->database" options.

The scientist/ mathematician/domain expert on the other hand often understands a domain very well and can isolate problems and even propose solutions but is often unable to translate those visionsinto reality for lack of professional level programming skills. To use the art analogy, this is like being able to visualize exquisite paintings, without the required skill to transfer that vision to paper.

The traditional solution to this seems to be for the domin expert and programmer to engage in "conversation" ( 'onsite customer' anyone? :-) ). But in my view this is like drawing a picture by putting a "visualizer" (who can't draw) and a "draftsman" (who doesn't have artistic insight)in the same room and asking them to produce a painting. It might work for Identikit pictures but you won't get any works of art.

Coming back to the original idea, Mathematics,like programming is very much a meta skill, in that one can use the expertise across multiple domains and problem sets. Unlike programming, mathematics often helps the practitioner to grasp the underlying essential nature of a domain.

To conclude, I am considering switching my (long planned) PhD to Applied Mathematics (from Computer Science), the reasoning being that I can always learn programming on my own while using the formal structure of a PhD program to hone my mathematical skill. Alternatively I could specialize in a field that combines mathematics and programming (like AI or Robotics). However that decision is still some way off. In the coming months, I hope to deepen my knowledge of both mathematics (Topology and Group Theory if anyone is interested) and programming (more AI and Programming Language Theory). I am now more convinced than ever that a combination of mathematical and programming ability is worth acquiring.

Wir sind alle Dänen

This is the rare "political" post. Those not interested, move right on.

Enough is enough.

In my opinion it is foolishness to initiate a "clash of civilizations". But if there is a battle line forming by virtue of some people insisting that their religious laws should apply to people of other religions (or no religion) then I know on which side I stand.

Anyone has the right to be "offended". That does not give them the right to kill, burn and issue threats. Fwiw, I do not believe in Islam, Mohammed, his "sacredness" or infallibility, etc etc. The people who protest most at this "disrespect" have laws in their own countries that officially forbid the practice of any other religion. If you carry a Bible or Bhagavad Gita into Saudi Arabia, it will be seized and shredded at the airport. How dare they protest against any "disrespect"? First practice this "respect to other religions" and then complain your religion isn't respected.

Kennedy once said "Two thousand years ago the proudest boast was civis Romanus sum. Today, in the world of freedom, the proudest boast is 'Ich bin ein Berliner.' All free men, wherever they may live, are citizens of Berlin, and, therefore, as a free man, I take pride in the words 'Ich bin ein Berliner!'"

Today, all free men, no matter where they live, are citizens of Denmark.

Wir sind alle Dänen.

Update: This post has generated a lot of feedback mostly by email (some people seem afraid to express themselves in public. hmmm...) .

One comment on this blog (subsequently deleted by the author) said "There's also the trap of 'they don't respect my religion/beliefs/whatnot so why should I respect theirs?'. That's the point where civilized conversation breaks down." .

This is a little naive. You can't have a conversation with people who don't follow the norms of "civilized" conversation and are not interested in a conversation. This most often happens with people who are convinced that their truth (religion/prophet/Holy Book/ideology/ whatever) is infallible. There should be no tolerance of the intolerant.

From an article by the editor of Jyllands-Posten (the Danish newspaper that published the cartoons) (emphasis mine)

"Has Jyllands-Posten insulted and disrespected Islam? It certainly didn't intend to. But what does respect mean? When I visit a mosque, I show my respect by taking off my shoes. I follow the customs, just as I do in a church, synagogue or other holy place. But if a believer demands that I, as a nonbeliever, observe his taboos in the public domain, he is not asking for my respect, but for my submission. And that is incompatible with a secular democracy."

So yes, this kaffir maintains that anyone who demands rights and respect that he is not willing to give to others is a hypocrite.

And while I may not (or may) be impressed with Islam or its Prophet, (that is my privilege in a free society), my stance is not anti-Islam but anti-hypocrisy.

People (of any religion) who say "respect my religion" should extend respect to other religions (and to atheists). There is no one way "civilized debate".

Old Laptop, Meet New Laptop

As you can see I am not too much of a photographer (the laptop screens are much duller in the photos than in real life. I have no clue why.) but the new IBM ThinkPad Z60m (on the right) is a very nice machine, much more so than the (now ancient) Compaq Presario 2100 (on the left).

Indians are cheap, not free!

When you are an independent consultant, you see a lot of crazy people. The most dreaded monster in this bestiary is that of the Non-Resident-Indian-Trying-To-"Develop Products"-In-Bangalore.

The game generally goes like this.

Some desperate Indian working in the USA on a regular job (note that he is NOT a venture capitalist, businessman etc) gets what he thinks is an "Awesome" idea. The he discuses this with some equally clueless friends and they hammer out some technology choices (j2ee , .net whatver). After a few weeks/months of this they decide they want the software done "cheap". Even companies which charge very little money per developer hour (say TCS) wouldn't give these folks the time of the day so they ask their friends in Bangalore to reccomend "top grade" independent developers.These poor innocents recomend people they know to be good developers and have left the corprorate rat race to work independently.

Now the fun begins. The Independent Consultant (IC from now) gets a call from the USA saying "MR X who you worked with in Company ... reccomended you as a top notch developer. We have this awesome idea that we need you to develop in "asp /.net" within 3 months. We also are looking for junior developers, testers and maybe a Project Manager. Do you think you can help us"? The consultant, if he has been independent for a while, has seen this dance many tims before and immediately asks "Do you guys have any money or is all this wishful thinking?"

There are a few different answers to this. Sometimes it is "yeah we can pay 5$ per hour for the first 24 weeks " ( I am NOT joking!!!). Or alternatively , "you see we are just starting out blah blah so we don't have much ready cash but we have all these highflying VCs lined up and if you can work free for the first 6 months then you have millions of dollars in equity".

Duh . Yeah Right.

Some of the more ... emmm .. subtle folks wants the IC to work for them without knowing what the "cool idea " is. After all a "cool idea" is very valuable right? We once encountered an "idea man" who offered to join our company as a "Project Manager" ("since it has been a long time since I coded anything") while looking for funding and in the meanwhile he would let us pay him an "industry standard" salary.

Stupidity is the one thing which REALLY has no limts.