It is growing exponentially with approximately 1 year doubling, but it accelerated in 2017.
There are other crypto currencies, probably of the same calculating power combined.
So total power of bitcoin net is 2 on 10power22 classical processor operation per second. This is approximately 200 000 more than most powerful existing supercomputer.
Markram expected that human brain simulation would require 1 exoflop. That means that current blockchain network is computationally equal to 20 000 human brains. It is probably enough to run superintelligence.
But most of it can’t do neural nets calculation. However, if the same monetary incentives appear, specialised hardware could be produced, which will able to do exactly those operations, which are needed for future neural nets.
If first superintelligence appear, it would try to use this calulation power, and we could see it by changes in bitcoin net usage.
TL;DR There is no hardware problems for creating superintlelligence now.
Some back of envelope calculations about superintelligence timing and bitcoin net power.
Total calculation power of bitcoin now is 5 exohash (5 on 10 power 18) https://bitcoin.sipa.be/
It is growing exponentially with approximately 1 year doubling, but it accelerated in 2017. There are other crypto currencies, probably of the same calculating power combined.
Hash is very roughly 3800 flops (or may be 12000), but the nature of calculation is different. Large part is done on special hardware, but part on universal graphic cards, which could be used to calculate neural nets.
https://www.reddit.com/r/Bitcoin/comments/5kfuxk/how_powerful_is_the_bitcoin_network/
So total power of bitcoin net is 2 on 10power22 classical processor operation per second. This is approximately 200 000 more than most powerful existing supercomputer.
Markram expected that human brain simulation would require 1 exoflop. That means that current blockchain network is computationally equal to 20 000 human brains. It is probably enough to run superintelligence. But most of it can’t do neural nets calculation. However, if the same monetary incentives appear, specialised hardware could be produced, which will able to do exactly those operations, which are needed for future neural nets. If first superintelligence appear, it would try to use this calulation power, and we could see it by changes in bitcoin net usage.
TL;DR There is no hardware problems for creating superintlelligence now.