Summary
mining POW = dQ/dt/dV
infrastructure cost of transaction confirmation rate = sum (sum (dE/dt/dV) dt ) dV
where
dQ = heat energy released = release rate of entropy at a given temp
dE = potential energy of system (infrastructure) = reduction of entropy in sum of space-time, if temp were constant
mining = "demonstrated intelligence of an individual" = competition
confirmation rate infrastructure = "total intelligence of the system" = strength of society
and where there is a government (protocol) that constrains and guides the first towards creating the second. Bitcoin's POW should be the first, but all that energy is being wasted. I totally disagree with the philosophy that all that energy is being well-spent in deciding who updated transactions first.
I wonder about love and hate: There can't be a reduction in entropy without an emission of it. Love requires emission of hate. Intelligence requires emission of ignorance. It required a lot of hate and ignorance in the past in order for mammals to have love and intelligence.
I'm working on trying to create a check-and-balance protocol where the interaction between users, nodes, and miners would create a constant-value coin. Users send a market price signal to miners by paying for coins, nodes send a market price signal by demanding fees, and I think maybe miners could send a signal to nodes by being able to invalidate a percentage of their fees. Maybe nodes could send a signal to miners by being able to change coin release rate (via coins per block or difficulty).
Derivation
I came across the above while pondering the possibility Bitcoin's USAF debate. The rest of this post is is a message I sent someone. It shows my thinking process that lead up to the above and mentions several different parallels.
There seems to be something deep in the debate. "POW" rewards the selfish individual and "USAF" thinking is like community trying to work together for a greater good. It's like capitalist ideology verses socialist ideology.
POW discovers a fact via might is right. It's not a consensus. Consensus is majority is right, even if 90% are weak and even if it is a bad idea. Might is right can also be a bad idea in the long run.
Intelligent consensus results in rules that maximize GDP of the system and median GDP of the individuals over the long run. POW, like marketplace competition, solves the question(s) that the consensus asks it to solve, by killing the losers. Killing the weak seems brutal, but it results in higher total GDP and higher median GDP. The individuals and the system become stronger. "Individual" could be an idea, a coin in a sea of coins, a business, or a person.
Fuzzy definitions can point the way to more fundamental axioms. so bear with me if some of these equivalences are an offense to a mathematical mind. See the quotes at bottom concerning mathematical rigor. Anyway, first bear with me and consider the very rough approximations correlations I have in mind:
POW=competition=individual greed=negative sum=capitalism without governing law=anarchy
"USAF"=consensus=cooperation=system-wide benefit=positive sum=socialism=democratic law
Ignore "USAF" if you don't think it's related to consensus.
There is a key to life in this. It's like determining when we should be selfish and when we should be "loving" (or "working together"). We should work together when there's an agreement on "what's best for everyone" and be selfish when there is a dispute on the protocol. It's the core of ideological disputes.
POW is not actually work because it's based on finishing first so it is proof of work / time = power (which is "strength" or "might"). Saying they have to expend a work to solve it is ignoring the time to solve is not a fixed, but depends on competition. POW is actually "proof of most work, faster than the others". So it should be called proof of power POP. The capital expenditure to get the power is an energy expense that creates a "potential energy" but the kinetic energy expense (electricity) per time at an assumed standard efficiency is what proves the power. Nodes also have a capital expenditure but they do not have to demonstrate power. So nodes are more directly related to a potential energy.
So my equivalences can be extended:
POP = kinetic energy spent per time = cancer hogging glucose
Nodes = potential energy existence = Amazon.com reinvesting all profits
To be more precise, the kinetic energy I'm talking about is converting potential energy into heat. So it's really a heat energy.
But each worker inside Amazon has to demonstrate POP in a way that is not cancerous. POP is an kinetic energy expenditure at a local point in time and space to arrive at a decision that does not care about the system-wide (in all time and all space) potential energy. You are asserting POP can figure out what's best for the system, but I do not believe it is true. You are saying USAF is being forced on everyone (force is a directed POP because time=i x space and P=F x space / time), but my perspective is that it's very gentle (non POP). That does not prove nodes (or USAF) has an Amazon-like intelligence that maximizes non-cancerous POP and therefore maximizes future potential energy of the system.
The above considerations result in two axioms that tie physics to social institutions.
capitalism = POP = selfishness = derivative of local heat energy generated = dQ/dt/dV
democracy = consensus = love = integral of system-wide potential energy stored = sum (sum (dE/dt/dV) dt ) dV
Via relativity, a space-time contortion is energy, so the above relations are fundamentally unitless, so it may be just a different way of saying: capitalism seeks higher rate of entropy emission democracy seeks maximal entropy reduction There can be no entropy reduction without an emission of it. Bad ideas must be released before good ideas can be retained.
So there is an important ying and yang here that I can't quite write a feedback equation for in order to design a protocol that implements it. Unchanging laws should seek system-wide long-term love by advocating constantly changing local instantaneous hatred. That is the socialist's view point. The capitalists viewpoint is the same, but it reverses time: Constantly changing local instantaneous hatred results in (no "advocation" needed) unchanging system-wide long-term love. The socialist believes we should be our own God. The capitalist either believes there is no God needed, or that God (nature) will take care of things without our help.
Continuing with the topic at hand:
Quotes against mathematical rigor: “The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it.”
"All physicists and a good many quite respectable mathematicians are contemptuous about proof."
"It is obvious that methods of the professedly rigorous mathematicians are sadly lacking in demonstrativeness as well as comprehensiveness."
"Those who may prefer a more formal and logically-arranged treatment may ... do it themselves."
Many non-math Wikipedia articles have been ruined by mathematical rigor.
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