Induction, Big Oh and Lies that computers tell us

December is here. I haven't posted in a while, so this one is gonna be a sweeping update.

The past few weeks, we have been focusing on Induction, and how to prove the property of a certain entity through proving it true for all such entities. It makes sense. I think... I enjoy the structured proofs of induction. It's not very complicated and you know what you have to begin with and where you want to get to. It's more of a puzzle than knowing the math pre-reqisits. I enjoyed doing the last three tutorial problem sets, and I think they went well.

Big Oh is something that I took to quite well. Again, the proofs that we deal with in class seem quite structured. It is kind of interesting to categorize functions according to their growth rates. Wondering what happens as something gets really really big, is something that is a universal phantom that everyone thinks about some time or the other in their lives. It kind of reminds me of this poem we did in school once.

How vague are all the mysteries
Which bind us to our earth;
How far they send into the heart
Their tones of holy mirth;

However, even though it kind of takes away from the imagination of math, the proofs feel safe, because you are in the realm of what you know, and you know what you need to do. I guess that makes it comfortable. So far, I would describe CSC165 as comfortable. I don't think CSC236 will be the same story though. That is left to see...

Most recently, we have been learning about expressing numbers in certain bases, and floating point representation of numbers. This is something familiar to me from my engineering years, although it was quite confusing back then. representing numbers in a different system shows its useful nature, but there is always the problem of compatibility and if you treat your mind as a system, then where is the balance between the number system of the mind, and that of the computer.

I also liked the idea of relative errors. Again, it's such a simple concept, just finding a percentage of the error with relation to your function, but it has such great implications. I like relativity because it's intuitive, especially when you talk about it in simple numbers. Einstein might be rolling over in his grave. So much for a lifetime of work...


p.s I hope to post more often between now and the 20th. Sometimes inspiration might just come in the form of a couple of more marks. No harm in being honest in a course about reflection and proofs.