Tuesday, August 29, 2006

Infinity Causes Infinite Confusion

For last 3-4 weeks I have been spending a hell lot of time on Orkut Mathematics community. And for last few days I have been finding a lot of posts on the topic of infinity. The confusion around the word infinity is so great that I was in total awe. Almost all the posts were way wrong about infinity. (I think most of the smart people who had no confusion probably did not bother to post.)

There was lot of discussion on things like 1/0 = inf, 1/inf = 0, inf/inf = 0, inf/inf = 1 and other confusing beasts. Most of the people participating in the discussion were mostly students of 11th and 12th grade from various countries. This is the time when most people meet infinity in their mathematics classes. (I also met it during the same period of my life, but more on that in some other post.)

The most common form of confusion was around 1/0 = inf. Most of the people argued that when we make the denominator smaller and smaller in 1/x, then the fraction gets larger and larger and when denominator x becomes equal to 0 then the fraction 1/x becomes equal to infinity. Now that's a highly absurd statement, but people involved are excusable because on their first date with infinity, almost everyone feels the same.

There were some posts by people were engineering graduates and I was surprised to find that they still had similar feelings about the beast. I don't think that is excusable because almost all engineering courses have some course in basic calculus. But anyway, the real culprits are the teachers, professors and worst of all, the book authors who fail to explain even the very basic concepts like infinity.

I really felt very sad about all this state and tried to help them in whatever way I could by posting a lot of stuff about infinity. I gave very simple example and explained in great detail. For some people I even scribbled in their scrapbook to remove the confusion. I guess it would help them.

I was lucky enough to get Hardy's book "A Course of Pure Mathematics" and I never had to worry about such issues. Please get hold of that book to save yourself from the horrors of infinity.

Sunday, August 06, 2006

Math @ Orkut - II

Orkut is gr8! Just gr8! When I joined the mathematics community 2 weeks back the membership was around 35800 and now its gone upto 36942. More than 1000 members in just two weeks. This proves that, contrary to the popular belief, mathematics is really one of most interesting subjects. This belief/myth seems to be popular only among those who never had any interest in studies as such.

The community is highly active. If you post something on a topic or create a new topic, you are guaranteed a response within few minutes (sometimes even 2-5 minutes). Looks like on the other side of the web there are people desperate enough to share ideas, solve problems and have discussions (like myself on this side of the web).

The chances of learning new ideas/solutions is very high. In college days when I found some interesting problem I used to try them with various approaches and I used to think I have found all the possible approaches to the problem. The members on Orkut Math community have taught me otherwise. I learnt new approaches to many problems of my college time. So thanks to those members.

There are some members who are in their formative years of +2 (12th grade) when they don't have access to good books and seem pretty confused by ideas of modern mathematics. I really feel very much obliged to help them in every way to clarify their doubts. I remember my +2 days when I was not satisfied by the presentation of modern mathematics in textbooks and used to search library for better books. My eyes were opened by Hardy's Pure Mathematics and I now feel like helping others opening their eyes because they also seem to be trapped in a situation similar to mine some years ago.

And next we have this group of real geniuses who have done (or are currently pursuing) postgraduation in maths and computing from reputed institutes in India and foreign countries (and BTech from IITs). They have studied a hell of advanced math of which I have no inkling. I am eager to learn whatever I can from these guys (guys in wider sense, not only for males). Meanwhile one can also find some bright undergraduates who are nothing short of genius.

And lastly we have some members who want their "5 minutes of fame" by posting some obvious paradoxes like 1 = 2. Even they are given a warm welcome in the community. After all who knows something nice might come out of these paradoxes. And anyway I like to clarify doubt and confusion whenever I can. There are some simple and dumb questions posed by genuine members who are really confused because of a lack of solid foundation. And I hope they probably get their fundamentals right after reading posts from the community.

The joy of creating something is very real and great, but the joy of admiring someone who creates something is no less. We have this joy of creation as well as admiration on orkut. And the passion of some members here cannot be expressed in words.

Finally there is this nice consequence: My friend count on Orkut has now become a strictly increasing function of the number of days I am spending on Orkut.

I hope there are many readers of my blog who share the same passion and enthusiasm for mathematics as myself and I invite them to join the orkut math community.

Wednesday, August 02, 2006

Meebo Me

Now you can contact me if I am online at Meebo. Please send your message using the widget named "Parama" on the right sidebar. This is an important feature provided by the Meebo guys.