User blog:Edwin Shade/A Common Hyperbole

There is a common hyperbole I hear, which takes the following form: "Wow, that took for-ever !" If people just had a hint of an idea as to how long forever really was, I think they would still use this hyperbole, but perhaps use it more sparingly. For when it comes to comprehending the scale of large numbers, the best aid is that of time, more specifically the amount of time you have experienced as a person.

Though I have the feeling many Googologists consider themselves to be able to imagine numbers such as a googol or $$10\uparrow\uparrow 10$$ with ease, they still are not comprehending the true size of the number. What many people fancy themselves to be imagining when they imagine a million is a square with a side length of 1,000 on each side. What is actually being imagined is not a collection of objects where each object is clearly imagined, but rather a vague, amorphous 'form' of a collection of objects. Even if one was exposed to a vast collection of objects, one could not use that as a reliable method of visualizing large numbers, because the laws of perspective and optics would dictate that beyond a certain distance individual objects would become blended into each other, creating once again, a 'form' of a collection of objects.

So it seems then that our most powerful tool for understanding large numbers is not by spatial intuition, but by timescales. Consider, that while beyond a certain distance objects fade, there may be an event that has remained in your mind for decades. Older ones have no trouble in comprehending longer time scales, and hence would have a better grasp of numbers like a billion if it was translated into "the number of seconds in about 32 years". To imagine a billion objects is an impossibility, but to imagine a billion seconds is easy, if you've lived at least 32 years that is.

Assuming an unlimited lifespan, our perspective of numbers would surely change, as numbers like a trillion come into our grasp of comprehension, (after 31,709 years). Why, after 120,000 years, the lifespan of a long-lived tree, (about 400 years), would seem to you to be as ephemeral as the seasons are today ! After 20,000,000,000,000,000,000 years, the rise and fall of a mid-sequence star would appear to be as short as we regard a bolt of lightening nowadays. Ultimately then, visual analogies are limited, but time is what can afford us the greatest perspective of large numbers.