Tuesday, October 28, 2008

Impossible problems and successful approaches: Story of Fermat’s Last Theorem

Fermat’s Last Theorem: When do people commit themselves to solving seemingly impossible problems? And how do some of the successful ones approach such problems? Let’s explore these 2 questions with the example of how Prof. Andrew Wiles of Princeton solved Fermat’s Last Theorem (called FLT henceforth) 14 years ago on 25th October 1994. When Andrew released a manuscript presenting the proof of FLT, it was a significant event in the history of mathematics. It put to rest a problem which remained unsolved for 357 years in spite of various attempts by top mathematicians of each century. (Source for all the information is a classic book from Simon Singh: Fermat's Enigma.)

Moment of commitment: Andrew’s affair with FLT began at the age of 10 when he found the problem in a book in a library. By the time he entered graduate school in Cambridge, he had studied all the past attempts to solve the problem. However, FLT wasn’t an acceptable topic of study towards PhD. As Andrew says, “The risk of working with FLT was that you could spend years getting nowhere”. Andrew’s PhD supervisor, Prof. John Coats, suggested that he should work in an area called elliptical curves. A turning point came in summer of 1986 when Ken Ribet of Berkley proved a strong linkage between a conjecture called Taniyama-Shimura (TS) conjecture and FLT. This effectively meant, to prove FLT all you need to do is to prove TS conjecture. TS dealt with two disjoint areas of mathematics elliptical curves and modular forms, one of which Andrew was already a known expert. When Andrew heard this news at a friend’s place, he knew, “At that moment that course of my life was changing … It meant that my childhood dream was a respectable thing to work on. I just knew that I could never let that go.”

Andrew weighs affordable loss: Andrew says, “Of course the TS conjecture had been open for many years. No one had any idea how to approach it but at least it was a mainstream mathematics. I could try and prove results, which, even if they didn’t get the whole thing, would be worthwhile mathematics. I didn’t think I’d be wasting my time. So the romance of Fermat which had held me all my life was now combined with a problem that was professionally acceptable”.

Andrew’s approach: Andrew knew that any serious attempt on the proof could easily require ten years of single-minded effort. For the next 18 months Andrew spent time familiarizing himself with every bit of mathematics that had ever been applied to, or had been derived from, elliptical equations or modular forms. He also knew that anything to do with FLT generates too much interest and that could distract him. He made a remarkable decision to work in complete isolation and secrecy in his attic. For the next seven years Andrew was to make a series of extraordinary discoveries, none of which would be discussed or published until his proof was complete.

Andrew on moment of insights: “Often you write something down to clarify your thoughts. In particular when you’ve reached a real impasse, when there’s a real problem that you want to overcome, then the routine kind of (mathematical) thinking is of no use to you. Leading up to that kind of new idea there has to be a long period of tremendous focus on the problem without any distraction. You have to think about nothing but that problem – just concentrate on it. Then you stop. Afterwards there seems to be a kind of period of relaxation during which the subconscious appears to take over, and it’s during that time that some new insight comes.”

To summarize: People commit to seemingly impossible problems when two things happen: (1) The problem is close to their heart (e.g. childhood dream in case of Andrew) and (2) Affordable loss doesn't look intimidating anymore. Serious players are in the game for a long haul (e.g. Andrew committed 10 years for the problem) and spend significant time in sharpening the tools (18 months in case of Andrew). Do check out the striking similarity between Andrew's view of how insight occurs and what we presented in Innovation trigger: idea vs insight.

Friday, October 24, 2008

Insight, entrepreneurial mindset and principle of affordable loss

Separating insights from non-insights: Let’s say your organization has this tool where employees, customers, partners log ideas. And you are part of this committee that selects ideas from this pool of ideas to be taken to the next stage. Now, you have read somewhere (perhaps in Innovation trigger: idea vs insight) that ideas with insights are better candidates for selection than ideas without insights. So you ask the question: How do I know which of these ideas came with insights from the authors? Let’s see if understanding of a species called “entrepreneurs” known for its commitment to one or more insights helps us here.

Entrepreneurial mindset: Let’s say our friend Seema realizes one day that it would be great if there is someone who home delivers simple meal on a need basis in the evening in her neighborhood. There may be enough number of working women who might use such a service. Seema might take any of the following approaches:

  • Approach-1: Analyze the market (go around in the neighborhood with a questionnaire), do the cost benefit analysis for various demand points (50 meals a day, 100 meals a day etc), rent from the place where she needs to operate, employment cost etc. And eventually see what all she needs to start the business. Seema might say I need at least Rs. 5 Lakh to start this business considering all the rainy day scenarios.
  • Approach-2: Talk to a few friends and see if any of them would use such a service. A couple of friends actually show interest and Seema starts supplying them the evening meals. She operates from home. After a couple of months the number grows to 10 meals a day. Her menu slowly stabilizes, she gets a hang of negotiating with suppliers etc. After a year and 70 customers Seema rents a small place to operate this business.
Well, according to Prof. Saras Sarasvathy of Darden School of Business, Univ of Virginia, most of the entrepreneurs go with approach-2 (see What makes entrepreneurs entrepreneurial?) and she calls the principle behind this approach as “Principle of affordable loss”. Unlike approach-1, where you ask “What all do I need before I jump into this?”, principle of affordable loss asks, “What can I afford to lose before I get further clarity?” Note that in approach-2 your destination can keep changing. For example, Seema may find out that instead of ready meals, her customers value packets of fresh cut vegetables more and she may focus on that service rather than meals.

How does Principle of affordable loss help? Let’s go back to our original question: How do I separate ideas with insights from those without insights? You say to the idea owners: Well, we don’t have the luxury to allocate separate time for ideas. Only ideas with prototypes qualify for selection. Now, only those people with insights (and deep conviction) are likely to spend time say over the weekend (or afford to lose something) to come up with a prototype. Or if you are a Google, you will say: Take 20% of your time off to show me a prototype but make sure you meet your current project commitments. We know what that means.

Tuesday, October 21, 2008

Innovation trigger: Idea vs insight

Where do I start? One question that invariably comes up during my innovation workshops is: “Where do I begin?” And when I throw the question back at the participants, one typical reply comes, “Start with an idea”. Let’s do a simple thought exercise. Ask yourself “How many ideas did I come across last week?” These ideas could be your own or you saw them on TV ads or in meetings or a friend told you etc. I am sure the number will be in 10s if not more. Now ask yourself, “How many ideas did I pursue?” We know what the answer is. A couple of months back I co-moderated a strategy planning exercise along with a colleague. A number of seemingly good ideas came up during the day. However, when it came to taking ownership for execution, people starting looking at each other. So here is a fundamental question: What is it that makes some people pursue some ideas some times and not do anything other times? Is it possible that this thing called “idea” is, after all, not the starting point of innovation?

Insights about “insight”: Let’s turn to a distant cousin of “idea” called “insight”. An insight is that “Aha!” or “Eureka” moment when you are convinced the problem is solved. What does science say about insights? Psychologists and neuroscientists have found out following essential features of “insight experience” (see Eureka Hunt):
  • Phase-1: First phase is called “preparatory phase” where brain devotes considerable power to the problem. Many times we call this “focusing on the problem”.
  • Phase-2: What happens next is “search phase” as brain starts looking for answers in all the relevant places.
  • Phase-3: The next phase is when the brain “gives-up” or reaches an “impasse”. While solving word puzzles, this happens in a few seconds.
  • Phase-4: This phase is what scientists call the most important phase and it is the phase of relaxation. During this phase the cortex seeks out more distant associations in the right hemisphere. As Jung-Beeman says, “That is why so many insights happen during warm showers”.
  • Phase-5: This is the last phase where the brain connects and restructures existing information (dots) and sees the same old thing in a completely new way. Miller, a neuroscientist from Princeton says, “Once that restructuring occurs, you never go back”.
So what? You are a lot more likely to pursue “insights” rather than “ideas” because they come with strong convictions. And the best place to start is with those problems which are pain in the neck today. Because, only for such problems you are likely to give undivided attention (or focus). And finally, don’t forget phase-4: the relaxation phase. Now, I am not surprised that most of my moments of insights have come when I am jogging.

Sunday, October 19, 2008

Centenary of a blue ocean: Ford Model T

Blue ocean: This month, 1st October to be precise, marked 100th birthday of Ford Model T. It was 100 years ago that Ford Motor built the very first of the iconic gasoline-powered automobiles to be sold. By the time formal production halted in May 1927, more than 15 million had been built. Model T created a blue ocean, a new market for affordable cars built through standardization. Till then the custom made cars cost around $1500, twice the average annual family income. In 1908, the first model T cost $850. In 1909, it dropped to $609 and by 1924 it was down to $290. In comparison the price of a horse driven carriage, the car’s closest alternative at the time, was around $400.

Challenges: I liked this tour of Model T pictures. I particularly liked the above picture as it depicts difficulties associated with blue oceans. While the cars came out, roads weren’t ready. I am sure the same would be the case with gas stations and service stations. Creating an eco-system in the new market while continuing to make profits is a characteristic of blue ocean winner.

Ocean turns red: Over the years, blue ocean starts turning red (competitive) and from it new blue oceans are created. For example, in 1924 GM introduced "a car for every purse and purpose" and in the 70s Japanese introduced small, fuel efficient cars. Today, the ocean has turned bloody red (fiercely competitive). Ford and GM, the heroes of the automobile revolution, are struggling to keep afloat. And yet, out of this red ocean, a player called Tata Motors is trying to create a blue ocean for ultra low cost cars. Perhaps one of your great grand daughters will create a similar picture gallery of Nano in 2109.

Thursday, October 2, 2008

Indian Robot Olympiad (South Zone) experience

What happens you toss creativity, collaboration, competition and loads of fun together with school kids? I am sure there won’t be one answer to this question. However, what we experienced at Indian Robot Olympiad (South Zone) last weekend at Indus International school can’t very different. Kids from 40 schools in Bangalore, Kodaikanal, Ooty, Mumbai participated in the event.

This picture shows a practice session on the playing field for primary school category. The robot which has just left the start line should follow the dashed line, pass through the gate and topple 3 cans kept in three corners (first one is at bottom left corner).

This is a practice session in junior high category. The track is more difficult due to stair-case and other hurdles.

For making & programming a robot, kids used Mindstorm kits from Lego. It was the first such event in the southern part of India and I am sure it will catch on in the coming years. For coverage in The Hindu check here and that in Times of India here.

Wednesday, October 1, 2008

Bangalore innovation forum and Pasteur’s quadrant

Bangalore Innovation Forum Launch: We had the kick-off event of CII organized Bangalore Innovation Forum at IIMB last Wednesday (23rd Sept). Kris Gopalkrishnan, Chairman of the forum, presented his vision of making “Bangalore an innovation hub”. Prof. Balaram, Director of IISc, gave a special address on the role of basic and applied research in innovation. I am summarizing below what I understood from Prof. Balaram’s talk.

Pasteur’s quadrant: There are some basic questions when it comes to research and more importantly funding research. This is especially important for policy makers. If you have Rs.100, how much to allocate for basic research (which may or may not have any real life application)? And how much to allocate for applied research? Typical assumption is that one can focus on either of these but not both. Donald Stokes questions this assumption by creating following 2x2 in his book “Pasteur’s Quadrant: Basic science and technological innovation”:

Bottom left quadrant represents most of us (“common-man”) who are doing neither basic nor applied research. Top left quadrant is epitomized by Niels Bohr whose work in quantum mechanics was inspired solely by understanding “what is?” rather than “what is useful?” Bottom-right quadrant is epitomized by Edison who worked (and extremely productively) on only those areas which are useful (like light-bulb). Well, what is not commonly known, is that Pasteur has made significant contribution to both basic research (crystallography) and applied research (pasteurization process). The question is: how can we make Pasteaur’s quadrant more populated? It is interesting to ask this question at a time when American economy which epitomized its emphasis on basic and applied research is going downhill in spite of all the funding. See recent Businessweek article: Can America invent its way back? (end of Prof. Balaram's talk summary)

Bangalore innovation ecosystem: Forums such as this can go a long way in strengthening the innovation ecosystem. It was evident from the discussion that various academic institutes, research institutes, industry and government are all working in isolation. Currently the participant profile looked more “engineering and researchy-type” (an important element of the ecosystem). However, I hope it becomes more diverse over a period where brand managers, product managers, psychologists, sociologists, neuroscientists, venture capitalists, government representatives etc. participate. Looking forward to it.