Definition: The Satoshi Coefficient

[5EC948A1]

The Satoshi Coefficient can be defined as follows:

http://latex.codecogs.com/gif.latex?\LARGE S = \frac{ Hn^2}{E}

Where for any time period:

H is the hash rate
n is the number of hashing nodes in the network
E is the energy consumed to sustain the hash rate

The Satoshi Coefficient is a value that can be used to rate the quality of a distributed crypto-currency network.

[bg002h]

The Satoshi Coefficient can be defined as follows:



Where for any time period:

H is the hash rate
n is the number of hashing nodes in the network
E is the energy consumed to sustain the hash rate

The Satoshi Coefficient is a value that can be used to rate the quality of a distributed crypto-currency network.

You could raise any term to any power...why pick the ones you did?

[5EC948A1]

I chose to follow Metcalfe's Law:

http://en.wikipedia.org/wiki/Metcalfe's_law

[WiW]

You could raise any term to any power...why pick the ones you did?

... used to rate the quality of a distributed crypto-currency network.

That way the number of nodes parameter has more weight - to signify a more distributed network.

What I'm not getting is what is the energy consumed parameter for? I would switch it for a parameter that tells the mining income, to signify a more competitive network. Throwing in more electricity does not necessarily make the network more or less secure or distributed - an excess of energy output could be spent by either honest miners (better) or dishonest miners (worse). Less profit margin means more competition.

[5EC948A1]

I am pleased to provide the first estimate of the Satoshi Coefficient using the following values from Blockchain.info about the Bitcoin Network.

http://blockchain.info/stats

H = 110,559 GH/s
(E will be estimated from Blockchain's 650 watts per gigahash)
E = 100,559 * 650 = 71,863,350 W/s
(n is determined from "nodes connected" at http://blockchain.info/connected-nodes)
n= 1175

Satoshi Coefficient estimate = 2,124

[5EC948A1]

I think energy is an important part of the coefficient because it is a fundamental way in which we measure work. The Bitcoin network brings together mathematics and energy (work) in an amazing process. I think the Coefficient is a way to try to quantify this in an amazingly simple formula.

[puffpuffpass]

I think energy is an important part of the coefficient because it is a fundamental way in which we measure work. The Bitcoin network brings together mathematics and energy (work) in an amazing process. I think the Coefficient is a way to try to quantify this in an amazingly simple formula.

good job. now go get a life.

[odolvlobo]

What does this number measure? What do you mean by the "quality" of the network? There are a number of criteria that could be used to evaluate the quality of the network, such as the resistance to a 51% attack, the maximum number of transactions, the number of nodes (or n²), or the average time to propagate a transaction, or its energy efficiency (H/E).

[puffpuffpass]

What does this number measure? What do you mean by the "quality" of the network? There are a number of criteria that could be used to evaluate the quality of the network, such as the resistance to a 51% attack, the maximum number of transactions, the number of nodes (or n²), or the average time to propagate a transaction.

stop pretending you care

[odolvlobo]

What does this number measure? What do you mean by the "quality" of the network? There are a number of criteria that could be used to evaluate the quality of the network, such as the resistance to a 51% attack, the maximum number of transactions, the number of nodes (or n²), or the average time to propagate a transaction, or its energy efficiency (H/E).

stop pretending you care

stop pretending you don't

[WiW]

I think energy is an important part of the coefficient because it is a fundamental way in which we measure work. The Bitcoin network brings together mathematics and energy (work) in an amazing process. I think the Coefficient is a way to try to quantify this in an amazingly simple formula.

I still don't see how energy output relates to the quality of such distributed network. If E is high or low, it's because of global electricity prices or hardware efficiency (available globally) respectively. As such, an attacker is usually affected by E as much as honest miners.

[5EC948A1]

What does this number measure? What do you mean by the "quality" of the network? There are a number of criteria that could be used to evaluate the quality of the network, such as the resistance to a 51% attack, the maximum number of transactions, the number of nodes (or n²), or the average time to propagate a transaction, or its energy efficiency (H/E).

Its a calculated number that just uses simple but important metrics. I would speculate that if there was another network right now with a Satoshi Coefficient of 3,000 it would be beating the Bitcoin Network right now. Yes, that network's coins be more valuable than Bitcoin's. Its just an idea, but I think it shows how the Bitcoin Network should be improved: more hash rate, more hashing nodes and less energy. If you follow this thinking out some, it results in a very interesting substrate.

[bg002h]

So, S=n^2/650

It will be interesting to see if this parameter pops up naturally in some equation somewhere.

[5EC948A1]

So, S=n^2/650

It will be interesting to see if this parameter pops up naturally in some equation somewhere.

Of course I used a value for E that I could obtain quickly (650 from Blockchain.info) to calculate the first ever estimate of the Satoshi Coefficient. In reality, determining E precisely is quite difficult. The interesting aspect to this new coefficient is that it lays the groundwork for a new network to efficiently compete with the Bitcoin Network by focusing on optimizing H,n and E to get a better coefficient than Bitcoin's. However, the Bitcoin Network quite naturally is working to increase its Satoshi Coefficient. In fact, a certain network topology, node feature set and energy source is the logical outcome. I think that's enough info for now, I've already given away valuable information. Enjoy the Satoshi Coefficient. :-)

[chriswilmer]

I like the idea... but I also see the use of energy in this calculation as not particularly meaningful.

As it is, it's more of a measure of energy efficiency than anything.

So, let's see, the simplest measure of energy efficiency is hash-rate over energy:

S = H/E

I think if I were to propose a "distributed quality" coefficient, it would be:

S = n^2/H

Honestly, I think that's what you wanted. If the hash-power is very concentrated, you will have a very low number. The problem with this coefficient is that it weights all nodes equally.

S = (n1*H1 + n2*H2 + n3*H3 + ... ) / H^2

Now that would be much better (every node multiplied by its individual hashing power), although much harder to calculate.