The great 20th Century philosopher Douglas Adams once said that we are, in a very important sense, protected by our own ignorance of scale – for if we were ever to successfully conceptualise the actual vastness of time and space, and ourselves in relation to it all, the shock would kill us. Adams conceived that a device capable of producing such an effect, even momentarily, would result in the most horrific torture imaginable to whoever was on the receiving end, but only briefly because their brain would be instantaneously annihilated. He called this machine the Total Perspective Vortex.
The universe is big. So, the kind of people who try to measure things of impossible bigness have to use impossibly big numbers that are purely theoretical. Nobody really understands these numbers because our brains are busy protecting us. It’s a futile exercise to even attempt to find words to express just how incapable we are of understanding true scale.
So, here goes.
First we need a big number. A googol is a usefully ridiculous number to begin. A googol is 10¹ᵒᵒ. The term was coined by a nine year old in 1940, so it wasn’t a spelling mistake (later a couple of American guys would give their new tech company a name befitting something truly awesome of scale and vision – it was they who made the spelling mistake). A googol looks like this:
1000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000 (ten with 100 zeros after it).
This is already confusing because it is fucking insane, but immediately after conjuring the googol, as if the point wasn’t made, the same kid and his uncle the mathematician came up with the googolplex. This now makes the googol look positively sensible.
The number, googolplex, is a one, with googol zeros after it. Simple. Of course, this is already way past theoretical. Writing the number itself would of course prove problematic, after first working out that you would need a stack of notebooks with a mass far greater than that of the observable universe. No worries though, because to write the number would take an estimated 1.1×1082 times the accepted age of the universe.
Already our brains have closed down, because they love us and they don’t want to explode. Some very smart people have tried to come close to explaining it though. Celebrated excellent genius Carl Sagan gave it a go, saying something about the number of combinations of ways to arrange individual fine dust particles, if you filled the entire universe with fine dust (one googolplex, give or take).
We understand then, logically, nothing is or can possibly equate to one googolplex of anything. So…
In 1980 some guy called Graham came up with another number. This thing was way, WAY bigger than the googolplex. There clearly wasn’t any point in going further, so Graham had. A lot. The crazy thing about this number (we haven’t gotten near crazy yet) is that although there is no way to physically represent it, which would melt any supercomputer that tried, we somehow know that it is a whole, finite number. Not only that, we know that an expression of this number would contain, somewhere inside it, a row of ‘threes’ several million miles long. We also know, because the math people tell us, that the number is divisible by three and ends in a ‘7’. Graham liked his number a lot. He called it Graham’s Number. Even the ‘Guinness Book of World Records’ liked Graham’s number and validated it as being at least as amazing and pointless as everything else in those books.
At this point, termed by me just now, ‘The Continuum of Batshit Insanity’, we reach the illogical conclusion. It is indeed just too much.
None of these numbers multiplied by each other or anything else comes anything close to TREE(3). This is something that apparently is also a real, finite number. I have no idea how we can know this, because of the fact we also apparently know that there isn’t enough space in the universe for a solved proof, or time left in the universe to do it. Wise old mathematicians warn energetic young mathematicians to stay the hell away from this monster, and the exuberant young mathematicians become tired and grey, having given their lives in vain to that ever-elusive breakthrough, just out of reach.
So, I guess, if you’re ever feeling down, or just wondering, ‘What is the purpose of it all?’, well… Jeebus, don’t think of any of this stuff. This is a fucking nightmare.
“If life is going to exist in a Universe of this size, then the one thing it cannot afford to have is a sense of proportion.” (Douglas Adams).