Last night, I gave a talk for the BlinkBl-nk 7 event which happened in Blu Jaz. The talk is a recollection of what culminated to my doctoral thesis in cosmology and some after-thoughts about the subject years later. I share my thoughts on the subject here in this blog and share with you the synopsis of the talk as follows: Modern ideas in theoretical physics revolve around the concept of extra-dimensions and the attempt to unify the four fundamental forces of nature with string theories. Our Universe has been a great & extraordinary laboratory where we formulate hypotheses to disprove these ideas. Can we find extra dimensions via the cosmic microwave background radiation left over from the first three minutes in our Universe? How do we test such an idea using modern satellite technologies like Planck and WMAP? The story started from a doctorate thesis & ends with a satellite that has been recently launched into space. [Read more...]
Sometime back, while reading Fazlollah M. Reza’s “An Introduction to Information Theory“, I revisited a solution that I have sketched out years back on the Eddington’s controvery problem. This problem is interesting to me because it exemplifies the type of confusion that existed in probability prior to the introduction of set theory considerations. Eddington is the same astrophysicist who did the solar eclipse experiment to demonstrate the prediction of light bending using Einstein’s general relativity. I thought I should share the solution which I co-solved with Yen Lee, an old friend from Cambridge who’s now a postdoc in Purdue University. To quote the problem, “If A, B, C, D each speaks the truth 1 in 3 times (independently), and A affirms that B denies that C delcares that D is a liar, what’s the probability that D was speaking the truth?” Historically, this problem was examined by M. Gardner in an article entitled “Brain Teasers that involve Formal Logic” and to everyone’s surprise, some theoretical physicists and mathematicians are embroiled in getting the correct the number of the solution. So, I will discuss the problem in detail, giving my solution to the problem and explain why Eddington’s answer of 25/71 was greeted with so much protests from the thinkers of the time. (Warning: If you are not a theoretical physicist or mathematician, you will be inundated by a plethora of mathematical symbols, hence you are warned before proceeding to the interesting parts). [Read more...]
Recently, while flipping through a research paper made me think about the estimation of π (which we know is 3.141… ). Here is an interesting problem which is associated with a method to estimate π. A needle of length a is thrown on to the plane covered with equally spaced parallel lines with seperation b. What is the probability that the needle will cross a line? How can this be extended to a random curve of length A? I thought I might just share a simple mathematical solution for both the Buffon’s Needle and Buffon’s Noodle problem that I have worked out years back on this problem during my PhD years.