User blog:Acamaeda/An Upper Limit to Googology

This is not meant to be a valid Googolism as much as an idea about Googolisms themselves. Mathematically, there is no limit to Googology. There might always be a more powerful method for defining big numbers, and even if there is one "best method", there are still larger definable numbers via naive extensions. In an ideal, theoretical world, the largest defined number could keep going up forever, but we live in a finite world with finite limitations. Defining numbers and systems for defining numbers uses information, and there is only so much information that can be worked with. Even if the universe is infinitely large, it won't last forever, and information can only travel so far in that time. This means that there are a finite amount of expressable valid Googolisms, and one of these must be the largest.

This upper limit, which we will call "Terminus", has not and will not be validly defined. In fact, it could be argued that the value decreases over time as the remaining lifespan of the universe decreases. What it does is give us a perspective of what's really possible. "Infinity" is a vague and indeteminate thing, there is no scale to work with when thinking of it as the upper limit. As our knowledge of large numbers grows, our idea of infinity moves with it. Terminus reminds us that we can't really go on forever, but also gives us a clearer sense of just how far there is to go. The amount of information defining even the largest and most complex Googolisms, even including all underlying systems, is incredibly small compared to the total information available, and is probably not even the most efficient use of the amount of information it does use. Every time a new largest valid Googolism is defined, we are no closer to infinity than before, but we are closer to the ultimate ideal of Gogology. Thanks to other limitations of the real world, we will never actually reach Terminus, but we can try to get as close as we can.