Ricercar Infinitum

The theme of by blog is to think. Perhaps some of you or perhaps all of you know about Descartes famous remark "Cogito Ergo Sum". I think, therefore I am. Essentially, he was saying he himself exists because of the very fact that he has the ability to think. Of course, to think is an abstract notion. Can a computer think? Can you think? We may try to pin it down as such, because if you can think, you can certainly think about thinking. And you think about thinking about thinking. Or you can think about thinking about thinking about thinking. Maybe you can think about thinking about thinking about thinking about thinking. And so on. An ethereal concept as been given form and identity by the capability of self-reference.

To see how an infinite regress of self-reference as a life of its own, we can see how to derive the concept of integers. Everyone should perhaps be familiar with an empty set. {}. The empty set as zero element. Now, consider an set that contains the empty set. {{}}. Such a set has one element. Next, consider a set that contains a empty set and a set that has an empty set.{{},{{}}} This set has 2 elements. Following this, we can consider a set that contains an empty set, and a set that contain an empty set, and a set that contains a set that contains an empty set. {{}, {{}}, {{},{{}}}}. Such a set contains 3 elements.. Ah, do you see, we have managed to create numbers from nothing. Creatio Ex Nihilo. Creating something from nothing. By doing this an infinite number of times, we can get all the integers that we can get. Numbers have been given existance by the concept of zero and infinity.

Infinity. That is another tricky concept. Infinite carries with it the notion of forever. Therefore, there is no upper limit to infinity. One question, is 0.999999999999...the same as 1? Maybe you will think that well it cannot be quite the same, because it will always lack the extra 0.00...001 before it can become a true blue 1. But on the other hand I also iron clad proof that 0.9999999...is 1. First of all, take 1 divided by 3. The result number is 0.3333....or can be expressed by the fraction 1/3. Now, if you multiply the decimal expansion by 3, you get 0.9999..But if you multiply 1/3 by 3, you get 1. So, this implies that 0.999..must be equal to 1. Sounds interesting? Similarly, 1.0000..001 with an infinite number of zeros in between, is also equal to one. So every number will have this spread of values around it that is equal to itself. This is almost sounding like Heisernberg's Uncertainty principle. You cant seem to pinpoint the exact location of a number on a number line!

Lastly, I want to end off with the "Zen-ish" concept of relative changes. Think of a flag. When the breeze comes, the ripples appear across the flag. Is the flag moving or the wind that is moving? Perhaps it is the mind that is moving.