A simple NAS
Last updated
Last updated
The existing arrangement for these blocks is a linear chain, which results in a space of dimension 1 x n where n is the number of confirmed blocks on the network. As the number of blocks is currently over 800 000 and forever increasing, this creates an extremely long and thin ‘world’ which has little application.
NASs provide a solution to this problem by arranging blocks into more useful worlds. For example, we could rearrange the first 10 000 blocks into a grid of dimensions 100 x 100 to be used in a game environment.
The problem is that this choice of 10 000 is itself arbitrary; our use of base 10 or indeed any number system is arbitrary as far as the bitcoin network is concerned (bitcoin code uses several bases including 2, 10 and 16; the original bitcoin address format is Base 58).
The bitcoin difficulty retarget period is 2016 blocks. This is a non-arbitrary number for the network, as the difficulty target is static throughout this time, and is recalculated and updated at the end of each period to ensure the current mining hash rate results in the average block creation interval trending towards (or meeting) 10 minutes.
This number is also relatively large compared to the number of blocks currently mined. As shown in the table below, a width of 2016 blocks creates a usefully proportioned world already, and won’t approach a ‘long skinny’ world for the best part of a millennia.
So if we use a width of 2016 is a good choice since it is both non-arbitrary and useful.
| Block height | Event | Proportions* | Real-world area (sq km)† | Date |
|---|---|---|---|---|
*Includes partial row where required †Assuming each block is 100 x 100 m
With a width defined by the retarget period, each row of the grid now has one uniform difficulty. It therefore becomes an x-axis variable which is the count of retarget period. Likewise, the y-axis now measures blocks since difficulty retarget.
This creates perhaps the simplest NAS, shown below:
823 785
Last blocked mined in 2023.
1:4.3
8 238
Dec 31 2023
4 064 256
‘Square’ world.
1:1
4 064
~2086
6 929 999
Last mining reward issued.
1.7:1
6 930
~2140
40 642 560
‘Long skinny’ world.
10:1
40 642
~2781
