(February 16, 2018 at 8:43 am)Succubus Wrote: It was definitely a wtf moment when I read that the volume of the entire universe, all 90,000,000,000 ly diameter of it, couldn't hold enough ink to print that number. And apparently that analogy is out by a very large factor.
It's completely, utterly insane.
It is actually *so* much worse than this.
Graham's number is the result of a tower of exponents of 3. So, for example,
3^3=27,
3^3^3 =3^27=7625597484987
3^3^3^3=3^7625597484987
This last (with only four 3's) is large enough that it is immeasurably more than the number of hydrogen molecules that would fit into the universe if they were all packed side-by side.
Now, Graham's number is the end result of a sequence of 64 steps, each *immeasurably* more than the previous one (much worse than comparing 1 to the number from four 3's above).
The *first* stage of this 64 stage of this process is found by constructing an exponential tower of 3's in four steps. The *third* step in this construction of the *first* stage is an exponential tower of size the number above. That is the number of 3's in the tower.
So, not only is is is not possible to write out Graham's number with enough ink to fill the universe, it isn't even possible to write out the tower of 3's in the third step of the first stage in the construction.
