Category: math

Posted on

Back to basics with Linear Algebra

At work, we’re at a point where we’ve come into possession of a huge volume of data – data that is just begging to be sliced and diced, with the promise of unveiling secrets that lay unbeknownst to us for now.

My brief fling with Machine Learning along with conversations with a respected colleague led me to explore Singular Value Decomposition (SVD). The application of this technique supposedly played a significant role helping team “BellKor’s Pragmatic Chaos” take home the Netflix Prize.

So I started at the wikipedia page for SVD and found myself clueless as soon as the first equation appeared. No worries. Taking a step back, I find out that SVD is a factorization technique within a branch of mathematics called Linear Algebra.

Linear Algrebra it shall be.

My daily train commutes, where possible, have found me following the MIT lectures of one sufficiently old and distinguished Gilbert Strang teaching Introduction to Linear Algebra. The lecturer I never had.

I’m also having a go at working through the course textbook Introduction to Linear Algebra and doing the chapter-end problem sets. So far, I’ve started to grasp vector arithmetics, and some cursory idea of computing matrices. As a bonus, the concept of “singular, un-inversible matrices” has emerged in Lecture 3.

Hopefully I’ll have this SVD thing down pat in due time.

Posted on

Six hundred thousand

I boarded the Flinders Street train heading back to the city at the end of another work week. Sitting right across my usual spot on the train was a young girl, no more than 7 or 8 years old. She was holding up her little toddler brother while her mother spooned what would appear to be the final teaspoonfuls of pumpkin puree into the little baby brother’s mouth.

Daughter was very chatty. The whole time, they were discussing a game that both were playing. It involved breeding dragons, hatching eggs and collecting dragoncash, treats, gems (after a bit of googling, I’m led to believe that the game in question is DragonVale).

On the topic of the resources that they’d stockpiled so far, daughter mentioned that she had accumulated more than 600,000 treats and was consulting mother as to what she could best use it for.

Six hundred thousand.

This got me thinking. When I was her age, I didn’t have any tangible concept of enumeration beyond perhaps a thousand. Given, there was a vague awareness of millions, billions and gogolplexes (which likely only emerged in my consciousness when I was 11 or 12 years old), but even they were just words we used in bouts of “who can say the bigger number”. I doubt I could’ve strung number scales together (e.g. “hundred thousand”, “ten million”), and I certainly hadn’t painstakingly amass 600,000 of anything,  even till this day.

I wonder what such an awareness does to a person, and how it will go on to shape the way one goes on to interprets the world around.

Posted on

Gödel, Escher, Bach: an Eternal Golden Braid

I’ve started reading this book because some smart sounding people think it’s a good book to make you sound smart too.

Up to page 72 now, and I’ve been introduced to self-referencing, Gödel’s Strange Loops, formal systems, proofs, typographical manipulations, meaning and interpretation, axioms and theorems.

I’m sounding smart already.

Hopefully as I read and blog, it’ll help me consolidate my learnings.