User:Sbiis Saibian

I'm an amateur mathematician and googologist, who is currently taking courses in computer science. I'm the creator of the popular "One to Infinity" web-book, and the inventor of Hyper-E notation. I've also coined a bunch of googolism's, such as the grangol, greagol, and godgahlah.

I've been fascinated by large numbers and infinity since I was in grade school when I first learned about mathematics. In 2nd grade I created my own extended series of large number notations in a naive attempt to provide an exact quantitative description of infinity. This has formed the basis of my modern Hyper-E and Extended Hyper-E notations. After my initial foray into large numbers, I didn't really get back into the subject until 2004. In December of 2008,  I launched my website, "One to Infinity". The title comes from the title of a small "treatise" I wrote as a kid on stapled scrap paper about very large numbers. Since then I've been expanding my site in the hopes of promoting a positive view of mathematics, and expanding peoples awareness of large numbers.

I am also interested in philosophy, including the philosophy of mathematics. At my core, I am a platonist. I believe mathematical truths can be made manifest in formula and symbols, but that the truths are independent of these manifestations. This belief forces me to accept the reality of an infinite set of finite integers, because given an unlimited amount of resources and time, every integer could be made manifest, at least in theory. Googology is then the exploration of the vast and infinite platonic realm of integers. We are simply plucking leaves from the "tree of integers" (the platonic plane) and bringing them down to earth (making them manifest). Some leaves are easier to reach than others, and given that there is an infinite number of integers, we will only succeed in highlighting but a small select group of integers amongst them.

My views on infinity are somewhat nuanced. Originally as a kid I had thought of infinity as a "goal post", which one could reach. As I've explored the subject of large numbers deeper however I've realized that that is a contradiction in terms. How can infinity, "that which is without end", end at infinity? In this sense, thinking of infinity as a completed process is meaningless and self-contradictory. As a kid I found the perpetual incompleteness of numbers frustrating, but I have over the last few years embraced this truth and realized that it needn't be viewed as an insurmountable obstacle. Rather, it's an opportunity for unlimited exploration. We don't need to reach a last number, and in fact I've come to the conclusion that this is anti-thetical to googology. Googology is not about reaching the end, ... it's about keeping it going. For this reason "infinity" is the enemy of googology. It's an excuse to say "infinity" and just be done with it. Most people are happy to dismiss googology, and simply say the largest number is "infinity". Having explored large numbers I've come to the realization, that infinity isn't even necessary to the discussion, in a certain sense. Consider this: If we removed infinity from the number line, how many integers would we have left? There is an infinite number of integers, even though they are all finite! If this is true than we don't need to even envoke infinity to continue our quest indefinitely, because no matter how long we carry things out, we would never carry them out forever. So it seems that infinity is something very ephemeral. It is somehow real and not real. It seems that in mathematics the notion of the potential to "continue indefinitely" is vital to is proper function, but completed infinities don't seem to be optional. I have opted to disregard the notion of completed infinities in googology. I like the sense of freedom this gives me, ... and this frame of mind gives a far more accurate idea of what infinity really is, than any other conception could have. If we are imagining a completed infinity, then we are thinking too small!

Because of my views on infinity I would be considered a constructivist. Constructivists believe that only mathematical entities which can be made manifest are real and meaningful. Although it seems like a contradiction in terms I'm a "platonic constructivist". I believe in the reality of things which can not be constructed in practice, provided they can at least be constructed in principle. Hence all the integers are just as real as 0 and 1, even though in practice we can't construct them all, but infinity is not real because we couldn't construct it even in principle without resorting to circularity (if we had an "infinite" amount of time, whatever that means). Just ask the question "when would we be done counting to infinity". The answer is "never" ... which means it's impossible, not that it just takes "a really long time".

This pretty much sums up my philosophy of googology. This is why people who are quick to end a large number competition by calling "infinity" urk me. Try and tell me precisely what number infinity is, and then maybe I'll not say it's just as bad as saying a "zillion" ;)