Hold infinity in the palm of your hand

Hellooooooo?

“I have this vision of hoards of shadowy numbers lurking out there in the dark, beyond the small sphere of light cast by the candle of reason. They are whispering to each other; plotting who knows what. Perhaps they don't like us very much for capturing their smaller brethren with our minds. Or perhaps they just live uniquely numberish lifestyles, out there beyond our ken.” Douglas Reay

Today I’m thinking about infinity as compared with the limitations of human understanding, specifically the limitations of my own understanding.
The universe is extremely big and the world of mathematics is vastly larger than both the observable universe and even any hypothetical mulitverse, even a relatively well known number like the googol (1x10¹⁰⁰) or one followed by a hundred zeros is larger than any metric used to describe the universe. A Googolplex (1x10^Googol) or (1x^(10x100)) one followed by a Googol numbers cannot even be written down using traditional notation within the confines of this universe. These are vast numbers but they are dwarfed by some of the numbers out there, in fact there are some numbers so vast that specialist notation is required to summarise them down in the confines of this real world universe.

If you’re really bored look up Graham’s Number here , which is the largest number ever used in a mathematical proof and also defines the largest range of numbers ever described. The large Graham number is the top bound of a range which starts at six. A real zero to infinity range as the Graham number is vastly larger than any number which can be conceived by the human brain which has about 10^(x10x16) combinations yet it starts at six. Six, a number which can literally be seen on two hands yet the Graham solution starts there and ends with a number so bonkersly large that I can’t write it down in any comprehensible summary form at all apart from the very unhelpful G₁= (3^^^3…3^^^3)⁶⁴ which means nothing to most of humanity (for more see Here for information on Knuth’s “up arrow” notation).

When you start to explore numbers outside of the realms of human comprehension it just reinforces our complete lack of understanding of the universe even though we have the tools to make explorations of the scarier ends of the logical realm, as Graham did. We’re like children looking into a vast cave exploring by the light of a tiny torch, finding interesting things and declaring “hurrah I’ve discovered Boyle’s law” or “Eureka! Energy does equal mass times the speed of light squared” and moving on to build our little houses of logical thought on the things our little torches are finding but of the darkness we still know nothing and there may be terrors lurking there to confound or destroy us. Yet we cannot stop looking, the universe itself is our home and we are parts of this universe, to understand ourselves, to understand where we live we must keep looking, even at the risk of finding something terrible.

Now as to why I started on this meandering journey through mathematical logic is that I was so bored confused during a endless meeting about data and service migration methodology, that inspired by an article on the ever fascinating io9.com, I started balancing my total lack of understanding about certain forms of esoteric data matching with my total lack of understanding about mathematics despite years as an engineer and maths geek. 

It got me thinking, certain areas of human endeavour, like Banking, are becoming trans-humanly complex, even the relatively simple stuff around account opening can be so complex that I've seen projects spend over ten man years on capturing all the permuations and there were still elements which weren’t defined or indeed definable. Things like complex derivatives and automatic trading algorithms are becoming so complex that no group of humans can describe it to another group of humans with total certainty and we haven’t got into the really complex stuff like genetic trading algorithms which can change and breed thousands of times a second and end up with successful designs no human would have come up with or even could come up with. It certainly puts my usual worries about requirements gathering into perspective.

“To see a world in a grain of sand, and heaven in a wild flower, hold infinity in the palm of your hand, and eternity in an hour.” William Blake