Seriously, what is this?

SSCG(3)? WTF?

So, you remember TREE(3)? It’s WAY, WAY BIGGER than that.

Now, to understand this, we need to know FRIEDMAN’S SSCG FUNCTION.

Information provided by Wikipedia and Googology Wikia.

A simple subcubic graph. If your first reaction was “What?” then you’re probably not alone. A simple subcubic graph is a finite “simple graph” with each vertices having a degree of at most three. So, no vertex in the graph is connected to more than three edges.

You know what? I can’t. here’s the links:

• https://en.wikipedia.org/wiki/Friedman%27s_SSCG_function
• https://googology.wikia.org/wiki/Subcubic_graph_number

SSCG(0) = 2. SSCG(1) = 5. SSCG(2) = 322293793. Nah, just kidding. It’s about 3.241704 * 10^{35775080127201286522908640066}, if I didn’t miss one. That’s insanely big, and that’s not even SSCG(3).

Yeah.

There’s also a similar function, SCG(n), and I don’t think it’s simple (see what I did? SubCubic Graph), and SCG(n) ≥ SSCG(3), but Adam P. Goucher could prove that SSCG(4n + 3) ≥ SCG(n).

Also, to put really large numbers into perspective, 1 billion factorial is approximately 1.57637137 * 10^8565705531, and that’s like nothing compared to even SSCG(2). Wow.

It’s huge.

For SCG(0), it’s 6. It grows. REALLY FAST.

Next time, we’ll be exploring THE FAST-GROWING HIERARCHY.