September 26, 2020
The incomprehensibility of Large Numbers
Humanity has accomplished a fair amount in a short time.
The Universe is largely considered to be something over 13 Billion years old. Earth's Homo-sapiens managed to go from basic agriculture to space travel in the span of twenty-something thousand years.
That's a respectable feat.
I still find it wondrous to imagine the unknown engineering necessary for building the Pantheon as civilization was really just getting started. And yet, imagine what the Romans would think of today's spacecraft, only another 2000 or so years later.
As humanity has progressed and knowledge has grown, the data necessary to understand that knowledge only expands in complexity.
Anchored to imperfect biological systems, humanity increasingly relies on the silicon world to bring the incomprehensible into focus. The calculations necessary for much in the contemporary world would be impossible without it. In this sense, the underlying numbers just represent a necessary measurement- the number itself is only a reference point to provide precision across measured entities.
In physical systems, there are no nulls.
Humans use abstraction to understand complexity and wherein numbers grow beyond some certain limit, it becomes incomprehensibly difficult to contemplate the relationship between entities in that system. It's very similar to reading Kant.
Such is a significant driver behind why humans have such difficulty comprehending exponentiality- the notion that a common piece of paper folded 42 times would reach the moon belies our terrestrial understanding of the universe. Humanity's internal calculator has limits we cannot inherently comprehend.
These incomprehensibly large numbers are still necessary in modern society, for defense systems, space travel, advanced agriculture, smart phones and so much more.
The universe is largely thought to be 90+ Billion Light years across, traversing it would require a considerable amount of paper.
Considering the distance to the moon to be about 1.3 light seconds away, you would need 2,215,111,986,217,081,000 pieces of paper folded 42 times to stretch from one end of the universe to the other. That would be 11,075,559,931,085.405 pallets of paper. If your supplier gave you a discounted rate for this paper of $1,200 per pallet, you'd need roughly $13,290,671,917,302,486. Ideally they'd round it down to only 13 Quadrillion dollars.
Scientific notation exists to work with such large numbers. Using such your paper supplier may send you an invoice for $1.3290671917303001e24 to make everything more efficient.
Incidentally, that's more paper than is available on the planet. Ideally, no reputable paper company would attempt to fulfill the order as such would cause catastrophic ecological collapse.