Proving the negative is notoriously hard (often impossible), and yet that's exactly what you're asking of me.
No, friend, game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers." Mathematical models are the very essence of being open to proof,
see here.
So, on one hand, you don’t need to provide any proof that non-mining nodes (or nodes) are irrelevant to Bitcoin’s security. On the other hand, you suggest that mathematical models make such proof possible. Then,
instead of providing any evidence of your argument, you link to an encyclopedia article about “Mathematical proof.” Really compelling.
No. That's retarded. Stop being retarded.
1. You tell me that hanging garlands of garlic on our front door is essential for home security, because stops Evol from getting in.
2. When I object & ask you to explain how, you retort with "so prove to me that garlic is
not essential for for our security."
3. I point out that such proof, as is the case for most "prove the negative," would be difficult, if not altogether impossible, and that the burden of proof remains with you.
So switching "padlocks thrown about on our lawn" for "garlands of garlic on our front door" proves your case....how? I provided numerous arguments that suggest this is an absurd analogy with no basis in reality.
I explained precisely how nodes are essential to network security. You've addressed precisely zero of those arguments. Here is a short summary that includes some of those arguments:
Every node must receive and process every transaction in every block. That distributes blockchain data to all nodes who enforce the rules, rather than a system where nodes trust a central source. [i.e. decentralization as a solution for the security faults of trust]
The more nodes that exist that are enforcing the same rules, the more likely the longest valid blockchain data that you receive from them is accurate.
If there are only mining nodes, the userbase, by definition, trusts miners. Hence why the existence of non-mining nodes secures bitcoin: by decentralizing hash power from validating nodes.
One of the primary determining factors in whether a Sybil attack is possible is how cheaply identities (nodes) can be generated. The more nodes there are, and the more decentralized said nodes are, the bigger the cost of mounting a Sybil attack, since attackers must set up more nodes in more distinct locations.
There have been past double-spend attacks by miners, so we know that rational miners will attack nodes if it is profitable to do so. That they have not used Sybil attacks specifically does not prove that it is not (and was not historically) possible to do so, but it certainly does not help your claim that non-mining nodes do nothing to secure the system. If they did nothing -- like padlocks on the lawn -- wouldn't that suggest it was cheap enough to attack them with Sybils?
Non-mining nodes obviously aren't impotent because we are talking about theoretical Sybil attacks, not historical ones.
In summation: Nodes enable a decentralized, trustless system to exist in the first place (securing users' funds from centralization failure). They are the system's defense against Sybil attacks (preventing double-spending and censorship attacks) from miners or other attackers. Further, nodes, by self-validating, also decrease the number and scope of attacks on users of the system by eliminating trust-based protocols.I conceded multiple times that "proof" in the realm of economics is elusive because economic models rely on unprovable assumptions about human actions. I therefore simply asked you to provide
any basis at all for your opinions, which you have yet to provide:
I go on to suggest that
Lol, that's where the root of your problem lies -- you think that "there's no such thing as proof in game theory and economics"
Claiming that "there's no such thing as proof in game theory and economics" is proof positive that you don't know what the fuck you're talking about, and are wasting my time.
Please stick to digging ditches & stop wasting my time, madjules007.
inb4 "But holy water": No, stop grasping at straws & keep digging.
Oh? Then state how game theory models are provable, rather than (as usual) stating a baseless opinion and trying to act smart. Explain please, with regard to epistemology, how mathematical models can
prove how humans will act. Go ahead and do it. What do "mathematical proofs" have to do with human action under non-repeatable conditions? That game theory employs applied mathematics to map correlations does not say anything about its capacity for proving
causality. Economic models are based on
tacit, unprovable assumptions about how the world works (e.g. human nature).
If economic models can be
proven, why are there no "Economic Laws" (as opposed to "Physical Laws")? Because variables in game theory and economics are tainted by human actions, which are governed by more than one simple variable that can be isolated and repeated in the empirical sense. In physical science, we can isolate variables in
repeatable procedures (experiments) to prove cause-and-effect. This is the accepted, rationalist approach. But in economics, there are no "repeatable" conditions -- the conditions are never the same.
Hume on the problem of causality in macroeconomics:
“There can be no demonstrative arguments to prove that those instances, of which we have had no experience, resemble those, of which we have had experience."Keep on insulting me. I don't mind. That you think that game theory models are "provable" and that randomly linking to a Wikipedia article about "mathematical proofs" makes your case certainly suggests that
one of us doesn't know what the fuck we're talking about.