Cool link, despite being a bit later than some of the other stuff on BB(6). Basically, it shows a 6-state Turing machine can encode a Collatz-type iteration:
```
a,b=8,0
while b!=-1:
b+=2-a%2*3
a+=a>>1
```
Showing that these halt or not are long-standing open problems, so knowing upper bounds BB(6) would immediately solve them (modulo a lot of compute time).
``` a,b=8,0 while b!=-1: b+=2-a%2*3 a+=a>>1 ```
Showing that these halt or not are long-standing open problems, so knowing upper bounds BB(6) would immediately solve them (modulo a lot of compute time).