The following is an excerpt from Information Theory: A Tutorial Introduction, page 65.
Now, supposing the identity of each letter in English does not depend on any letter that is more than 10 letters away. In practice, the dependency between letters diminishes rapidly as inter-letter distance increase, as shown in Fig. 3.6. Once the block length has grown to $N = 10$, the identity of every letter in a given block $B_k$ depends on other letters in that block and exactly two other blocks: the previous block $B_{k-1}$ and the next block $B_{k+1}$. All other blocks contain letters which are more than 10 letters away from, and therefore independent of, every letter in block $B_k$.
If the original text is sufficiently long, and if there are a large number of blocks, then the dependency between adjacent blocks just described accounts for a tiny proportion of the overall dependency between blocks. Thus, the more blocks there are, and the longer each block is, the smaller the dependency between blocks. By analogy, it is as if each block is one of a large number of independent super-symbols, and if the blocks are independent then finding their entropy is relatively simple. The only question is, how long do those blocks have to be to ensure that they are independent?
The block length beyond which inter-letter dependence falls to zero is called correlation length $N_C$. Once the block length exceeds the correlation length, it is as if all blocks are effectively independent, so increasing the block length $N$ beyond $N_C$ has a negligible effect on the estimated entropy $G_N$. At this point, $G_N$ equals the entropy of English; that is $G_N = H$. This matters because Shannon's theorems are expressed in terms of infinite block lengths, but in practice these theorems apply to any block length which exceeds the correlation length of the sequence under consideration.
Given some block, I can't see how block count decreases dependency on two blocks adjacent to it. Could someone, please, explain?