laver table This project only calculates up to the 256 x 256 laver table, since the next laver table (512 x 512) is too big to fit in a list. If you look at the period variable as the table resolution increases, you get the sequence (if you continued forever): 1, 1, 2, 4, 4, 8, 8, 8, 8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, . . . This sequence is non-decreasing, which means it never goes down. However, it seems to stop at 16. Will it be stuck at 16 forever, or will the sequence ever reach 32? Will it ever reach 64? 128? Will it reach any power of two? The answer to these questions is yes IF a very, very strong large cardinal axiom is true (specifically, the I3 rank-into-rank cardinal axiom). The divergence of the sequence has been only proven in ZFC + I3 to this date. However, it is not known if the divergence of the sequence isn't provable or refutable in ZFC alone, although it has not been done so yet. But IF the divergence of the sequence isn't provable in ZFC (which is likely) and ZFC + I3 is consistent (which is likely), then the laver tables hold the key to an extremely powerful function called q. We define q(x) as the number of tables you need to draw out before you reach one with period 2^x. For instance, based off of our sequence, q(0) = 0, q(1) = 2, q(2) = 3, q(3) = 5, and q(4) = 9. However, q(5) is extremely large - much larger than anything in the physical universe. q(6) is only larger; q(7), astronomically more than q(6). Remember that q is only total if ZFC + I3 is consistent.
gwaah #Laver table
