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7 Posts authored by: Burt Kaliski
Burt Kaliski

How Many Coin Flips?

Posted by Burt Kaliski May 1, 2010

For the past three years, I've had the privilege of writing up the annual "EMC Challenge" for the Massachusetts State Science and Engineering Fair.  The challenge -- typically a short series of math problems -- is given to students at the start of the fair, and a prize -- this year a $200 Best Buy gift card -- is awarded to one of the students who provides a correct solution.


This year's challenge was about probability -- see below for the questions and further below for answers.  (Congratulations to this year's award recipent!)


In addition to preparing the challenge, I've also had the privilege the last two years of serving as a judge, alongside several fellow EMCers and perhaps a couple hundred other volunteers from the area.  (One of those volunteers is my mom, retired New Hampshire science teacher Janice Kaliski, who is also past president of the New Hampshire Science and Engineering Exposition.)


Each year I'm inspired by the great ideas that the students have come up with and the way they've presented them.  The coming decades will be pivotal in terms of the application of science to global challenges and with students like the ones I've met at these fairs taking the lead, I'm increasingly confident that many of those challenges will be addressed effectively in new and creative ways.


Each year I also take back some ideas about how to improve EMC's own "science fair" -- our annual Innovation Showcase.  For instance, the idea of having separate sets of judges panels for each of the 30 finalists in our showcase -- rather than just one set of judges for the full set -- came from the state science fair's distributed approach.  Separate panels are the only way to scale to the hundreds of finalists that the state science fair has, but also turned out to be a perfect fit to a more modest number of 30 finalists at EMC last year who didn't gather in a central location, but presented online as the conference moved to a multi-site model.


A day spent in Cambridge is always worthwhile, the state science fair especially so.


__ Burt


EMC Challenge

Massachusetts State Science and Engineering Fair

April 30, 2010


A fair coin has an equal and independent probability of heads and tails on each flip.  It is easy to see that the expected number of coin flips until the first heads occurs is 2.


What about other situations?


  1. What is expected number of coin flips until two heads have occurred?  (The heads need not be consecutive.)
  2. Until both a heads and a tails have occurred?
  3. Until two consecutive heads have occurred?  Sketch how you determined the answer.


(see answers below)

















Answers:  Expected number of coin flips until:


  1. Two heads have occurred:  4
  2. Both a heads and a tails have occurred:  3
  3. Two consecutive heads have occurred:  6


Sketch of answer to #3: One answer (there may be others):


  • If first coin flip is tails – player must start over – prob. ½, 1 coin flip
  • If first coin flip is heads, second is tails – player must start over – prob. ¼, 2 coin flips
  • If first and second are heads, player wins – prob. ¼, 2 coin flips


Expected number of coin flips per round:  ½ x 1  +  ¼ x 2  +  ¼ x 2  =  1 ½.

Expected number of rounds to win:  1 / ¼  =  4.

Expected number of coin flips to win:  1 ½ x 4  =  6.

A newsletter that just appeared on the EMC web site [1] once again raises the intriguing concept of intrapreneurship.  Can you really be an entrepreneur inside a large company?  Can you have an "enterprise" within the enterprise?


I think the answer is a strong yes.  A large company is basically its own market for creating and advancing ideas.  In last year's Innovation Conference, more than 700 employees offered one or more ideas, and 3000 voted on them.  The ideas ultimately were "sold" to a panel of business unit CTOs and R&D center executives who acted as VCs and decided which ideas to invest in. 


Politicians spend a lot of time thinking about how to encourage entrepreneurship and investment in a region or technology space.  Executives do the same for intrapreneurship -- but have much more influence on the outcome. 


The Innovation Conference is one example of EMC's investment along these lines -- a way to create a market for ideas.  EMC Research Cambridge, which Rob Masson describes in the newsletter, is another way of encouraging ideas by connecting employees with the university research community. 


Steve Todd, also mentioned in the newsletter, is a classic example of an intrapreneur who  thrives in this environment.  He's been a top contributor to the conference and is also a driver of university research collaborations.  Steve makes the most of the investments in the internal "market" to move good ideas through the ecosystem.


The ideas and the inventors are already there -- it's just a matter of making the path to intrapreneurship a little easier.


__ Burt


[1] Intrapreneurial Intent:  A Newsletter for Innovators at Large Companies.  EMC, April 2010.

The EMC Innovation Network's applied research program has a two-fold mission:


  • Expand knowledge of key technologies and
  • Strengthen relationships with the communities who are pursuing them


As an academic researcher by training, I've picked up the relational part of the program from my colleagues over the years, and have grown to appreciate the value of just spending time with people who are working on new ideas.


That aspect was in full view during my recent trip to the West Coast where I had an opportunity to visit the Plug and Play Technology Center in Sunnyvale, California.  Kayvan Baroumand, the COO, explained that the center is more than an incubator of start-ups -- it's a "business accelerator."  (related video)  And the way it accelerates business is by bringing in corporations and VCs to spend time with the start-ups, formally and informally.


I was intrigued by the diversity of start-ups in the building and by the migration from cubes to enclosed offices as one ascends the floors of the building, mirroring in a way the ventures' advances through the stages of funding.


A number of my fellow EMCers from the Bay Area joined the tour, giving us some time to spend with each other thinking about new ideas.


As usual in research engagements, interacting with people around a new idea inspires creative thinking that can lead to new insights on internal projects.  The new idea itself might find a way into one of our projects, or it might not, but either way we're in a better position spending time with it.


__ Burt

Roger L. Martin and Jennifer Riel make the provocative observation in a recent Business Week column, "Innovation's Accidental Enemies," that management's demands for "proof" make it difficult for innovators to advance new ideas.  Indeed, the very term "proof of concept" suggests the importance of passing this management test.


I'm not so sure the corporate "enemies" are accidental.  In fact, I think the obstruction is there by design.  It's easy for innovators to come up with ideas, but only few will truly meet complex customer requirements.  A series of obstacles can serve as an early expression of those requirements, so that the ideas stay on target.  Good management ideally puts tests in the way to improve ideas.


I've also found that researchers sometimes present concepts to management as a solution that just needs to be invested in -- without laying out a plan for actually moving the business into the solution.  So, management's objection to an idea may not be an objection to the ends, but just to the (lack of) means.


One of the ways to put means and ends together is to get customers involved early on in research.  The Innovation Network research model looks for three-way partnerships -- universities, internal R&D and customers.  The customers help to keep the research on track and also provide a path for advancing promising concepts, which may be all the "proof" that is needed.


__ Burt

Wired, in the January 2010 article, The Neuroscience of Screwing Up, makes the usual observation that successes in research often emerge from initial failures (example:  astrophysicists Arno Penzias and Robert Wilson couldn't get rid of the noise in their radio survey of the Milky Way, only later to find that they'd discovered echoes of the Big Bang).


The point that struck me is a pattern for turning failures into success:  "The best way to solve a problem?  Try explaining it to somebody outside your field."


Author Jonah Lehrer reports University of Toronto lab director Kevin Dunbar's findings that "most new scientific ideas emerged from lab meetings" and that a diverse lab -- with representives of multiple disciplines -- can be more effective at problem-solving than a group of researchers all having the same training.  (Penzias' and Wilson's insight came from a casual conversation with nuclear physicist Robert Dicke.)


EMC's locally networked approach to research -- bringing together participants of multiple business units and university researchers -- fits very much this cross-disciplinary paradigm.


Prof. Busnaina's recent lecture is a good example of the benefits of these kinds of conversations.  Although the research area is nanotechnology, his problem-solving paradigms, presented at a high level, encourage creativity in other system design patterns.


I was especially impressed with the solution he shared to the problem of toggling a carbon nanotube switch between two positions, for instance to store a bit.


In previous approaches, a strand of nanotube material would be toggled between the two positions by applying a voltage to one of two circuits, one below and the other above the strand.  When a small voltage is applied to the circuit below the strand, the strand is pulled down toward the circuit, and remains there after the voltage is removed.  To pull the strand up again, however, would require a much larger voltage across the circuit above the strand, partly because the strand is now further away from that circuit, and also presumably because the strand is “locked” in position.  (My lack of precision on these terms illustrates Dunbar’s point:  As a non-expert, I need to communicate in metaphors.)


Busnaina’s solution is based on a simple motivation:  If pulling a strand down is easier than pulling it back up, is there a way to toggle the switch by pulling down two different ways?  The answer is yes:  If the strand is sits across the two circuits rather than between them, and rides over a divider between the circuits, then toggling is just a matter of activating one circuit or the other.  When a small voltage is applied across the first circuit, the strand is pulled down to that circuit and away from the second.  The pulling away is mechanical not electrical which is why it is easier than in previous approaches.  Similarly, when a small voltage is applied across the second circuit, the strand is pulled down to that circuit and away from the first.


I'm not sure to what extent Busnaina explaining these things to people outside his field last week helped him solve further problems.  Having it explained to me, though, may well help me solve other problems in the future.  I’m looking forward to finding the next problem closer to my own research areas that can be solved by putting together two easy operations rather than an easy one and a hard one.


__ Burt

One of the best ways I've found to learn a subject is just to listen -- really listen, without email and web browsing in the background (hard to do these days!).  In technology research, sometimes the listening involves reading a research paper, and sometimes hearing a research lecturer, which is what I look forward to doing every few weeks through the EMC Research Cambridge Lecture Series, now announced here on


This Friday, I'll have the opportunity to learn about nanotechnology and its future impact on storage and computing from EMC Research Lecture Series - Cambridge: February 12, 2010: High-rate Directed Assembly for Applications in Electronics, Energy and Life Sciences.  The lecture is open to the public (both in person and by phone).  It will be interesting to find out more about Prof. Busnaina's lab and the discoveries at this particular layer of "middleware" between atoms and everyday materials.


An hour or so with a talented commuicator on a compelling topic can help break through a surface understanding, and begin to explore.  It's one of the reasons that research lectures are so important in the EMC Innovation Network.  Listening and learning helps us to start taking things apart, so we can put them back together again in new ways.


__ Burt

As my colleague Stuart Miniman mentionedWelcome to Early Preview of the Innovation and Research Community, the innovation and research community at EMC has taken up residence on Labs.


It's an honor to be part of this space that Randy Ziegler and his team -- especially njain -- have put so much time into preparing.


Randy and I were both members of the company's Chief Development Office a few years ago when Randy was leading the Developer Network (of which this EMC Community Network is an outgrowth) and Jeff Nick gave me the responsibility to lead what he named the EMC Innovation Network, the company's new corporate research program.


It was clear then that the developer and innovation communities had a good deal of common interests.  The addition of innovation and research content to Labs is thus a natural next step.  Indeed, this home for so many great development activities is just the right place to share highlights of the company's Innovation Conference, publications by its researchers, and much more.


So, we're started.  Our goal is to more just sharing information, but inspiring creative conversations about what we've called, in the Innovation Network Lecture Series tagline, "the information infrastructure of the future."  I look forward to the journey!


__ Burt

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