# A response to Jonald Fyookball’s article “Mathematical Proof That the Lightning Network Cannot Be a Decentralized Bitcoin Scaling Solution”

I am assuming you’ve read or are familiar with the article referenced in the title: https://medium.com/@jonaldfyookball/mathematical-proof-that-the-lightning-network-cannot-be-a-decentralized-bitcoin-scaling-solution-1b8147650800

In a general sense, it’s claiming that the lightning network, Bitcoin’s second layer solution to scaling, will fail. He claims that this can be proved mathematically, which is the ultimate and rigorous end to disputes.

I don’t really have skin in the game here because I am interested in appropriate scaling solutions for cryptocurrencies like Bitcoin instead of hyping any particular coin. He makes a serious effort to analyze the technology and he comes to an unusual conclusion so I am naturally inclined to check it out.

The tldr here is he overestimates the negative externalities of centralization for layer 2 scaling solutions so he concludes the only viable topology for the lightning network is a completely decentralized one. The mathematics he whips out is largely unnecessary because it’s intuitively obvious that a completely decentralized lightning network requires unreasonable financial overhead (because you have to open payment channels with every person you transact with and each payment channel requires a minimum of two on-chain transactions).

Here’s a blurb I wrote about this on Facebook to someone asking about it:

The kindest way I can put it is like this: he’s grossly overestimating the negative externalities of centralization in a layer 2 solution in a careless way. One of BTC’s core value propositions is censorship-resistance, which is generally inversely proportional to the level of centralization.

The author is arguing that LN centralization compromises censorship-resistance, so the only topology of the LN would have to be completely decentralized. I agree that in a completely decentralized topology the LN wouldn’t be an effective scaling solution. I don’t need to read his mathematical argument to understand that. It absolutely is an effective scaling solution with a somewhat centralized topology (like the internet). So it’s sufficient to just address the censorship-resistance stuff.

In the absolute worst case where every country coordinates to own and monitor LNs (extremely unlikely), you can just transact on chain. (That’s why layer 2 solutions cannot be an existential threat.) For this kind of centralization to be a problem, it has to be generally infeasible for people to use in practice due to that censorship. For censorship to make LN fail as a concept, supernodes would have to

(a) all coordinate in perfect unison with no defectors

(b) massively censor LN participants to the extent that huge swaths of people find that they cannot use the LN at all and are forced to make transactions on chain.

Both of these things happening is extremely unlikely. Supernodes will exist in many different jurisdictions and I don’t see widespread, unwavering cooperation to all forms of censorship. Not to mention it only takes one defector to break this wall of censorship. I don’t see why a supernode couldn’t run over TOR, so even if govts tried to censor, they’d have a hard time doing so. Supernodes would pop up and disappear just like darknets. Also, I don’t see censorship happening on huge scales either. If supernodes were regulated, why would govts care to censor ordinary transactions? Govts usually censor very narrow things, like donations to [Wikileaks], or transferring money to some sanctioned company, or stolen funds like WannaCry. This wouldn’t force a huge percentage of people off of the network- it would just push all the transactions you can’t make with a credit card or PayPal to on-chain transactions (or supernodes on the darknet).

One last thing — he said something about routing of payments to be an issue. The topology of the LN is going to be similar to the internet we have today. Since routing packets across the internet is not a problem, I don’t see why routing payments would be a problem, either.

What’s interesting about Jonald Fyookball’s article is that he makes a bizarre assumption: The centralization of a layer 2 solution threaten’s Bitcoin’s property of censorship-resistance. It’s bizarre because (a) it’s extremely unlikely that supernodes in different jurisdictions would censor in a coordinated manner; (b) LN supernodes could be run over TOR, and they’ll probably be as hard to take down as darknet markets, which historically have required unusual resources by governments to deanonymize per darknet side (not a bad business model for darknets who are already sitting lots of dirty bitcoins); (c) that censorship would be so severe that a large percentage of participants would find the lightning network completely unusable and would be forced to have all transactions on chain; (d) most important, censorship-resistance would be totally unaffected because anyone could just transact on-chain if necessary.

His article comes off to me as disingenuous. He makes a major assumption with brief justification of “censorship-resistance”. Upon inspection, his justification does not make any sense. Off-chain technologies can not negatively affect censorship-resistance because users do not need to use them in the first place. Then he uses almost the entirety of the article to go over the mathematics in detail of something that is intuitively obvious: opening up a payment channel with every person is burdensome. Mathematical proofs are dense and generally not fun reads. Most people are going to skim over his mathematics, see the fancy equations and dense arguments and think that there is some legitimacy in his conclusion because ** look at all the math**.

Seriously. He spends a brief moment dismissing the actual architecture of the Lightning Network in one breath because “censorship-resistance.” Then he spends the stark majority of the article with an easy strawman (LN as completely decentralized) and rigorously tears it apart full of unnecessary equations and mathematics that serve largely to make his analysis look more rigorous.

It gets stranger. Remember how he spent almost the entire article rigorously refuting that completely decentralized Lightning Network? Well it turns out that *everyone, including supporters of the lightning network, already agree that a completely decentralized lightning network is not an appropriate scaling solution*. To someone knowledgable about the LN, what they would need is a rigorous argument that a partially centralized LN cannot work. He did not provide that argument. Instead he brushed over the real topic worth exploring and focused entirely on a strawman. His article is not really going to convince anyone technical that Lightning Networks are bound to fail and they are going to wonder why he wasted his time with an unnecessary mathematical argument. However, to someone non-technical, his article looks pretty authoritative. Everything he says is true, accurate, and knowledgable (*except that one super impactful assumption he glosses over really quickly*) and justified with mathematics (wow!).

Last thing to mention: Jonald Fyookball is the sole developer for Electron Cash, the fork of Electrum (a lightweight Bitcoin wallet) that is made for Bitcoin Cash. Fyookball is arguing about the one big thing that differentiates Bitcoin and Bitcoin Cash: their scaling solutions. Bitcoin will scale with off-chain transactions (Lighting Network) and Bitcoin Cash will scale with bigger block sizes. Now that Bitcoin Cash has forked from Bitcoin, I am unsure why Fyookball cares about Bitcoin. If Bitcoin’s scaling solution is bound to fail, then surely people will naturally gravitate to the better engineered coin when the time comes, which will be soon. Instead, it looks like Fyookball is trying to disseminate misinformation about the lightning network to attract people who aren’t technical and don’t know any better to his preferred coin, a competing minority fork, Bitcoin Cash.