Estimation of the real Bitcoin cost through the Network. Part 1

People have been trying to estimate Bitcoin in a variety of different ways, producing enormous quantity of methods. Yesterday we’ve got acquainted with some of them, but let’s draw our attention to estimation of a network, as Bitcoin cannot exist without it. In fact, the problem grows from impossibility of application of the standard estimation procedures, like discounted streams of money, which does not mean zero cost of BTC.

Another one identification attempt

As we’ve already seen neither the states, nor many individuals understand BTC essence. We’ll try to sort it out on the basis of a popular definition of a share holding. Why? They provide their holders with legal rights to receive a certain benefit from the company (for example, profit shares) which are regulated according to the general rules of law. Bitcoins also give their owners certain practical possibilities (in particular, access to blockchain) which are regulated according to the mathematical formulas integrated in the network.

The most suitable definition for separate shares sounds like “shares are the means of granting of transferrable rights to get profit, possession of the company, or receiving benefit from it”. This notion fits Bitcoin structure very well.

Separation of definition based on logical principles

In fact, internal cost of a share holding depends on a company cost. The estimation of a share holding does not provide its comparison with other share holdings or assets of other types or summing up the cost of all separate shares to define the company cost. This approach makes it impossible to estimate unique attributes of the company (profit, free stream of money resources, competitiveness, etc.).

Instead of defining the share cost, they define the cost of the company, which is then divided into the number of shares. Hence, every share holding represents the share property right of possession of all company assets. In other words, the cost of every share is defined on the basis of a total cost.

Cost of shares cannot be estimated without determining the cost of the core business and that’s why it’s impossible to estimate the cost of Bitcoin without the base cost of its blockchain. The obvious lack of an unequivocal verdict in crypto community leads to infinite discussions of what the cost source is (subjective and objective) and whether Bitcoin is money. These and other similar questions naturally disappear with correct start of the estimation — with a network (which we’ll present below).

Network estimation method

Search of a way of computer network estimation became a subject of profound studies. Networks have acquired recognition as practically significant and useful worldwide since long time. Thus, their utility depends mainly on the size of a network which is defined by quantity of nodes or users. Small and useful networks has small (but not zero) value, while bigger useful networks feature exponentially growing value.

According to Metcalf’s law (which was initially published approximately in 1980 as a solution for network estimation), internal value (utility) of a network is proportional to a square of the quantity of nodes in a network. Hence, if the quantity of nodes doubles, the network utility increase four times, since doubling the number of nodes leads to quadruple increase in the quantity of possible unique connections between them.

According to Metcalf, the quantity of possible connections in a network is the indicator of its utility, and utility is a value indicator.

Metcalf’s law was criticised due to three principal causes. Firstly, the law considered primarily the total number of nodes (users), instead of active nodes. Thus, it has not provided the situation when a large network which is rarely used (i.e. consists of many inactive or low-active nodes) can be less useful, than a network of the smaller size with greater amount of active nodes.

Secondly, the Metcalf’s formula presumes that every node or user is equally valuable, which is improbable, according to Zipf’s law. Based on Zipf’s law, the first most active user of a network is, most likely, twice more active and valuable, than the second most active user; three times than the third most active user, etc.

Thirdly, the use of Metcalf’s law for the estimation of large and fast-growing networks requires execution of enormous large calculations (which will be shown below).

After correcting the formula, the experts and Metcalf assumed that, in the logic of Zipf’s law, the network value should vary not proportionally to square of the nodes number (as Metcalf has initially assumed), but proportionally to the number of nodes multiplied by the nodes number logarithm (so-called estimated metrics n·log (n)). Due to the reasons specified below, the estimation by n·log (n) method is most fitting to Bitcoin estimation.

Two values

Metcalf’s law and n·log (n) formula (hereinafter referred together as — “estimation metrics of exponential law”) are intended for determining the relative network value at specific moments, based on the changes of nodes and users quantity. For example, if the network node number doubles with initial quantity x, the number of nodes, according to both approaches, will increase more than twice.

These two approaches differ only by approximate increase calculations. But the main thing is that none of them allows to learn the internal network cost, except for the cases when the value of its utility at specific moment is already known. The one should have a reference value (x) which will become a key for transferring exponential metrics. For this end, the one should take the other indicators or just make some assumptions.

X factor of Bitcoin

Can we calculate a certain value of the Bitcoin network with the help of Metcalf’s law and-or n·log (n) formula at specific moment of time (x) on the basis of which we could then extrapolate previous or future values? Perhaps, yes, we do, though it’s probably a task only for real experts. Nevertheless, we can put forward some important statements about x value of BTC blockchain.

Firstly, we can assert it does exist. The chain of blocks of the first cryptocurrency has yielded beneficious results since the very start, though only to the persons who were close to developer team. It was effective as it worked on the basis of the unique protocol enabling to perform operations which were earlier impossible in computer networks. For example, with the help of blockchain, unlimited number of people (with manager access rights) have full access to the generally accessible database. Thus, they cannot change any entries which were introduced earlier (at least for them to remain unnoticed by the other users) and this database is not exposed to the centralized control. Yes, there are certain lacks, but the existence of work in normal conditions has made a real breakthrough in technologies.

To show you how it works — let’s imagine you want to arrange the anonymous voting among all everybody willing to vote in it using PCs or smartphones to learn whether Pluto should be considered as a planet or not. Besides, all voters should see every vote (but not the author) online, without the possibility to change another’s votes. How can you arrange it?

Before the emergence of Bitcoin network it could have been done in only one way. You should have involved a trusted third party (which would ensure no changes in votes and observe the other participants) that will place a voting database at its server, support its security and online results posting.

However attraction of such third party entails additional risk, complexities, and expenses. It’s quite probable the one can skip additional risk and expenses, if the thing is about the Pluto’s status, but what can you do of the third party, instead of tracing the voting results, is focused on tracing amounts at bank accounts of voters or performed payments?

In this case, concerns about propriety of involving a third party (for example, the bank), increase, don’t they? Therefore, we allow only trusted third parties (banks and organizations carrying out remittances, or any similar institutions) to play this role; thus, they have to obtain very expensive licences.

Moreover, license owners have to pass audit in the field of book keeping and finance every year; auditors pass external quality assurance, state and state-governed institutions (money circulation management, Federal reserve system, Ministry of Finance, state bodies of bank regulation etc.) additionally check and regulate the work of banks and undergo periodic inspections too (for example, inspections of accounting chamber of the USA). And that’s not all! Well-trusted and financially confident organizations with support from the federal government (Federal deposit insurance corporation) should insure bank deposits against incompetence of entrusted third parties, thefts, or impossibility to bear responsibility.

Being the members of a society, we generously pay for services of these entrusted third parties and for regulation and control allowing to enhance the trust of citizens to them. Nevertheless, we get disappointed in them regularly.

It should be noted that thanks to blockchain we can arrange the voting on the Pluto’s status and (on a large scale) securely trace the balance of user accounts without attraction of trusted third registering persons (or the corresponding auditor organizations and regulation bodies), which increases the account accuracy.

The phenomena of trust companies, intermediaries, stock exchanges, authorized registering bodies, conditional deposit managers, clearing organizations, remittance companies, banks, and similar institutions can simply disappear — blockchain is a new, elegant substitution requiring much less resources.

Blockchain is not managed or controlled by any centralized entity or natural person. Nevertheless, this incorruptible, censorshipless, generally available (at least for those who have coins) system provides a way for secure, reliable, accurate, and irreversible registration of events and transactions. Therefore, it will affect the financial institutions and trust intermediaries in a way the Internet has done it with bookshops, musical instrument stores, publishing industry, post, manufacturers and people engaged in processing of film, newspapers, advertisements, telephone systems, etc.

Wait for even more exciting technical details in the next article!

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