The TREE function is derived from a game of colored dots and lines that form “trees” and how many unique trees you can make, given a certain number of colors.
(I won’t re-hash the entire explanation of what it is, but I strongly encourage you to click the link and watch the videos embedded therein because it’s mind-blowing.)
But I will just point out that the TREE function proceeds as follows:
TREE(1) = 1
TREE(2) = 3
TREE(3) = not possible to enumerate. Not even possible to imagine if you spend as much time trying as I do.
It’s essentially TAO(3), per the quoted verse.
. . .
One interesting facet of TREE(3) is that while it’s proven to be finite, it has no upper bound. It has an enormous lower bound, i.e., it’s definitely bigger than some other indescribably massive number, but we don’t know its ceiling.
It’s how I imagine the universe — finite, indescribably large and without a clear boundary.
. . .
Infinity has a lot of similarities to zero. They are two sides of a coin. A polygon with infinitely many equal sides is a circle, which is a zero of sorts*. Infinite sides is the same as no sides. To have an infinite presence is to be nowhere in particular. A map of everything is a map of nothing.
*Equal-sided polygons with four, six, eight, 12, 20 and 100 sides, respectively.
It is the finite, the mortal, the particular that stands in contrast to both. Being somewhere in particular is markedly different from being nowhere or everywhere. Having a finite life span is dissimilar to living forever or never being born, both of which are unchanging states and lack meaning.
But what to make of something finite, yet without upper bound? Finite on the edge of infinity, bigger than you can fathom, never quite graspable. Neither one nor the other.
. . .
I read somewhere once — if I recalled specifically I’d link to it — that where the real action happens is on the boundary. The boundary between land and sea is the beachfront. The boundary between overly controlled and out of control is where art is made and legendary feats happen in sport.
Maybe the boundary between the finite and infinite also describes the unforgeable complex systems that govern everything from the stock market, forests and corral reefs to the interactions of neurons in the human brain. (The link is worth clicking as it shows how no amount of processing power can generate random numbers, but nature can.)
. . .
I’ve written about AI before and how I think it’s overblown. I compared AI to Graham’s Number and the Tao to TREE(3), and AI to the set of integers and the Tao to the set of real numbers.
Reality is too complex to be encoded in bits.
If you realize this, you know AI will always be just a tool. It ever-increasingly masters the map, but never the territory.
There is no singularity, we cannot build a simulation that ever approaches reality and there is no chance we’re part of a simulation unless you define it so loosely as to mean reality itself, which is to say nothing at all.