## Friday, August 02, 2013

### Pi - probability function to find a number in Pi's decimal expansion

Yesterday night I was watching a TV series, "Person of Interest" and there was this small wonderful speech about "pi" the irrational number in it.

This made me do a Google search to find some place where i can look-up my phone number in the decimals of pi and i reached this website http://www.angio.net/pi/piquery which allows us to do such a search in the first 200 million digits of pi. As such I was disappointed that I couldn't find my phone number of my wife's number. Anyway, after playing around with this application, i realized that numbers of length upto 8 digits can be found more or less in this app but finding a 9 digit number is rare and the we could just forget the 10 digit numbers. This made me think of a question (i am sure mathematicians must have wondered about this question many times before) that is it possible to build/determine a probability distribution function which can tell us that probability of finding X (some number with m digits) in the first N digits of pi is p(X).

I definitely have no idea about how to approach this problem. But would love to know whether such a function can exist, and if it exists then how or can it be determined (even in some limited form, let's say for the first billion digits of pi, etc), and if answer to that too is yes then what is that probability function? Would love to see any leads for this interesting nerdy problem :)

## Thursday, March 07, 2013

### Separating Assessments and Teaching/Content Delivery in Education Sector

In this century, role of education in an individual/child's life is set to change in revolutionary ways, both in terms of skills required and the way ideas and skills are taught/ imparted. While most of this revolution would probably focus on innovations in the way content is created and delivered/ taught, there is enough scope for innovation in how this skill training part gets connected with the job market.

This connection is either missing or not strong enough and that is evident now also with the advent of online course offerings increasing at an exponential pace. These courses democratize education in the sense of providing every connected individual with an access to content/ courses. But there is no certainty that the person who passed a particular course or got distinction actually knows that content well and can use that knowledge in praxis. This is because it can’t be ensured that no one is cheating and it is an honor code based certification assuming that students are not breaking the code.

In case of India (and probably in other developing countries too where number of colleges have increased exponentially in past 1-2 decades) there is another problem. Because of wide-spread malpractices among the student and teacher communities e.g. plagiarism, copying in exams, etc, it is near impossible to ascertain whether graduates of such colleges actually know (all or even parts of) what they claim in their resumes or transcripts. Only option is either to try the candidate and see if she can perform as per the expectations, or if the true caliber of such a candidate could be ascertained through personal networks of the employer. In both of these situations, we see a trust deficit problem hampering the market (for jobs) from functioning well.

Top ranked or elite universities solve this problem through the signaling effect they create in the resume of their students/alumni. For this purpose they have to maintain a reputation in terms selecting great candidates, train them well and then test them with rigor. As doing all these things together comes along with a lot of conflict of interests, only few universities have been able to do it all well and can uphold their reputation. This is also why these universities enjoy the credibility they enjoy today.

On the whole, there is a great amount of trust deficit in the market for skills and knowledge. A huge number of educational institutions' lack the ability to create a signalling effect for their graduates in the labor market through reliable assessments. We feel this gap could be filled significantly if some reliable third party/ies can measure and certify the skill levels of individuals in a transparent and competitive manner.

Such an authority would test the students and certify the scores. These tests would be standardized tests but not generic ones like mathematics, general knowledge, etc. These tests would be for specific topics, skills e.g. regression, content analysis, non-parametric methods, which are equivalents of college/grad-school level courses. A credible authority conducting such tests would theoretically be able to provide everyone an access to trustworthy certifications verifying their knowledge/skill levels on a particular topic within a broad discipline. In addition, same organization or others could also provide experiential/peer learning opportunities for the learners by coordinating study groups, but the primary objective of the organization would be to conduct various types of assessments of skills, competencies and knowledge expertise.