In physics we describe the motion of springs as harmonic oscillators. In theory, a spring can be displaced by distance x and it will oscillate forever reaching point x over and over again until an external force is applied. The force applied by a spring is very simply:

F=-kx

The constant k is a value that is unique for all springs of different shapes, sizes, and material. The motion of a simple harmonic oscillator can be graphed as such:

In practice we find that most physical springs are dampened oscillators. Springs see a damping force preventing it from ever reaching position x after the initial displacement. Dampened oscillators bring more complex mathematics into the fold:

Where c is the damping coefficient. A system is critically damped when the motion of the spring tends towards zero. The damping ratio is a ratio used to determine how close a system is to being critically damped.

Damping ratio

We can see the effects different damping ratios have on a system below, where the critically damped oscillator is shown when ζ =1:

You can see the damping force is dependent on the damping ratio, and you can read more about them here and here. This negative force is applied across the system and is the explanation for why in practice springs don’t oscillate in perpetuity. This is a very simple outline of what a dampened oscillation is.

What the heck does this have to do with Bitcoin?

We have entered day 5 of the Bitcoin hashwars. Day 1 saw a gigantic show of force by the ABC miners and we saw a high initial displacement x from the average BCH hashrate. This allowed the ABC chain to quickly grow in hashrate and prompted many in the ABC community to quickly declare victory and recommend users split their coins and dump “BSV”.

As of 3:30 PM UTC Nov 19th, 2018

This initial displacement of hashrate was a result of a large amount of hashrate moving from the BTC chain onto the BCH chain at a time when the BTC chain was 100% more profitable to mine than the BCH chain. According to Peter Rizun, Bitcoin.com paid to power the Hoover Dam for a few hours on this day. At this same time, ABC had quietly worked with exchanges to implement checkpoints to declare the chain safe from reorgs. All appears safe on the ABC chain to safely announce a chain split, right? If that’s the case, then why have The BCH Boys been constantly declaring those that are recommending users to split their coins of being reckless and irresponsible?

The act of mining the BCH chain (ABC or SV) at this time is insanely unprofitable right now. SV miners are mining at a huge loss right now with the hashrate they have pointed at the SV chain. ABC miners are mining at a huge loss while also having to pay out pool contracts for miners that would prefer to make a profit. For both sides, this is unsustainable. However, the strategy of both sides appear to have been quite different from the start.

The SV strategy appears to have been the opposite of the ABC strategy. ABC decided to give a gigantic show of force off the bat to get a decisive victory, while the SV miners seem to be content sitting back and waiting. This appears to have been the strategy from the start for SV. On Sept 27th, Calvin Ayre tweeted:

As recently has Nov 17th, Jihan Wu still appears to be warning about the possibility of SV miners overpowering the ABC chain:

With that said, Roger Ver has decisively declared multiple times on Reddit that “SV lost the hashwar”, while also professing that the hashrate being used to defeat the SV chain is coming from BTC whenever it is needed:

He specifically says “the finish line is in sight, but has not been crossed” for the ABC chain. ABC supporters seem content with this strategy and view it as a winnable one:

However, we must look at this strategy through an economic lense. Coinciding with the unprecedented spike in ABC hashrate was an all time low since the implementation of the DAA of the profitability of mining BCH vs BTC:

It cannot be overstated just how much money is being burnt on both sides in this battle. BitMEX has done their own analysis and found these numbers as of Nov 18th:

Assuming leased hashrate, the ABC miners have outspent the SV miners. According to the public records of Bitmain’s financials, they do not have a large holding of BTC like the holdings claimed by Craig Wright. Craig Wright has continually maintained that he is willing to sustain losses for up to 2 years while selling BTC to fund the BCH hashwar. A bull run across the cryptocurrency ecosystem (specifically the coins held by Roger Ver and Jihan Wu) is the only thing that can save the ABC miners from continuing to lose large amounts of capital.

I believe we are seeing a real life damping oscillation play out on the ABC chain with respect to its hashrate. The damping ratio is proportional to the economic costs of funding this hashwar where the actual damping is the regular economic costs associated with funding this war and critical damping is the point where the ABC miners go bankrupt:

Zeta is the damping ratio

The damping ratio, as far as we can tell, has a few factors:

How much BTC/BCH hashrate is owned by the miners

How much BTC/BCH holdings is owned by the miners

The profitability ratio of mining BCH/BTC

The price at which miners can dump coins across chains (BTC, ABC, SV)

Various external factors

You split, we bankrupt you.

Craig Wright

The ABC chain appears to have used up its show of might off the bat giving the hashrate its initial displacement of almost 9 Exahash. The economic costs of maintaining this hashrate has so far shown itself to be unsustainable:

The Bitcoin ABC chain

Of course, we could be looking at a Driven Damped Harmonic Oscillator, which accounts for an external force F_ext(t) which allows for the oscillator to maintain oscillation despite a damping force:

Driven Damped Harmonic Oscillator

However, as Bitcoin is a purely economic system, we would only expect to see F_ext(t) given a large influx of capital/hashrate that we did not see prior to the fork and in the days after. Do the ABC miners have another trick up their sleeve?

We have to ask ourselves why the SV miners have not taken the multiple opportunities that have been given to them to attempt to gain majority hashrate over the ABC chain. If the pre-fork charts are to be trusted, the SV miners have at least 5.4 Exahash, yet we have not seen this deployed since the fork.

Are the SV miners waiting for the ABC miners to reach critical damping before striking? Why did the SV miners not give an initial show of force similar to the ABC chain? Where is Rawpool who voiced support for SV? Which side appears content with letting this last as long as possible?

“If you want a war…

I will do 2 years of no trade. Nothing.

In the war, no coin can trade.

If you want ABC, you want shitcoins, welcome to bankruptcy.

It was nice knowing you.

Bitcoin will die before ABC shits on it. I will see BCH trade at 0 for a few years. Will you?”

Craig Wright to Roger Ver

The SV miners appear to be engaged in persistence hunting. One thing is certain: despite the insanely reckless rhetoric of multiple individuals who I will not name that have recommended users split their coins and “dump BSV”, this war is far from over.