ProjectBlog: Application of Metcalfe’s law to VRENAR Network Funding

Blog: Application of Metcalfe’s law to VRENAR Network Funding

Metcalfe’s law applied to VRENAR for funding purposes

This document presents the VRENAR Economic Business Case and justification.

The material here is part of the VRENAR system Concept Design. This is the primary document presenting the financial and business proposition from VRENAR to IOTA. If accepted this will be incorporated in the VRENAR white paper update. It is provided for the attention of the project potential funders; the IOTA Foundation [14,17], but it is also for the digest and/or reuse of those who might plan similar ventures, and any other interested parties.


The business proposition is to create the new VRENAR network, integrated with that of IOTA, and for IOTA to provide the bootstrap funding required to do this. The overall intention of VRENAR is to efficiently convert the human information of all users directly to value, which is added to the VRENAR community, and thus ultimately to the monetary value of the IOTA token, and to reward the proceeds of this directly to the users.

Document Purpose

This document is to give detailed knowledge to the potential investors of the very strong business viability of VRENAR, for the purpose of bootstrap funding, specifically of the extremely positive effect this will have on the value of the IOTA token.

It is normally important to be able to make a reasonable future forecast of the expected value of any new network built on Distributed Ledger Technology (“DLT”) [12] currency or network, in order to confidently put a figure on the likely bootstrap funding needed to start the new network. In

The analysis here focuses heavily on the concept of utility, which we define loosely as the “Metcalfe utility”. This applies both to the netoid population growth and square law value functions of Metcalfe’s law, though different equations and numerical values apply to its application in each case, the effect in terms of its influence on growth, and thus the value of a network token is profound.

The VRENAR System

VRENAR, (VR enabled AR) is a combined AR and VR based social media system, designed for the primary stakeholders, its users. The system is designed using industry leading Systems Engineering techniques normally reserved for large scale proprietary and defence systems. User functionality will commence with non-VR/AR social media integrated with an IOTA wallet per user, progressing to integrated VR/AR functionality. Characteristically, the system will provide all users with continuous rewards from the outset, throughout the lifetime of the system.

Core Arguments

First we establish beyond reasonable doubt that Metcalfe’s law accurately describes:

  • The population growth of social media networks
  • The population growth of crypto-currency networks
  • The perceived token value in terms of real life buying power, in crypto-currency networks

Then we compare population growths of crypto-currency networks with those of social media networks in terms of the Metcalfe netoid functions describing the growth rates and sizes of each and note the following:

  • Utility is instrumental in both the rate of adoption, and the extent of the adoption. Utility is intrinsic to the perceived value of the network.
  • The utility of a social media network is orders of magnitude higher than that of a Crypto-currency network.
  • Scaleability is fundamental to utility.

We conclude that the addition of a social media to a fully scaleable, public, free-transaction crypto-currency will result in the highest value token to date.

However we note also a degree of adoption persistence. Bitcoin, the first established crypto-currency remains dominant despite many later alternatives offering similar utility. An exception is Ethereum. The utility of this is distinctively higher than Bitcoin [27]. We deduce this is due to the Ethereum smart contracts functionality. Ethereum subsequently experienced a higher growth rate, until both solutions encountered scaling problems in early 2018, resulting in significant drops in the utility of both.

Similarly, we see users of the first social media, Facebook, mostly persisting with continued use. This is despite the appearance of several other social media offerings, and numerous controversial public enquiries of Facebook. It still remains the dominant social media network (At least in the Western World).

In our estimation, adding a token to an existing profit based social media [29] is not a viable competitive possibility to the concepts we describe here, due to the commercial limitations of requiring a return on investment for shareholders.

Research Evidence

Recent research [1,2,3,4,9,11,20] shows strong evidence that distributed ledger crypto-currency networks, despite market price volatility, behave reliably according to Metcalfe’s law. This is directly represented by the network token value, the mean value of which is proportional to the square of the number of users in the network, averaging out short term market manipulations.

This extends even as far as Metcalfe’s law being a reasonable indicator of whether or not a crypto-currency token value is subject of a bubble or trough in market value at any particular time.

With no other changes, such as changes in utility, the number of users in the network is the only factor affecting the token value.

The VRENAR proposal is to boost the utility of IOTA with the addition of new highly desirable functionality previously unseen in any network. The main effect of this will be to increase the network virality, and thus the rate of adoption, and the subsequent value of the token.

The VRENAR System

VRENAR is an immersive augmented reality based social media platform based on IOTA in Concept Design. This is deliberately designed at a holistic systems level to offer maximum utility to all users.

The project is most unusual amongst open source projects, in that it uses all of the techniques and tools of top-down Model Based Systems Engineering methodology perfected in the supply of proprietary large scale defence, commercial, financial, and industrial projects to define the project as a top level concept design, around the needs of the primary stakeholders. This is in contrast to most open source and social media implementations, which generally start as bottom-up developments, grown to address stakeholder needs, most often the system owners.

In the case of VRENAR, the primary stakeholders, and the system owners, are its users.

The system Concept Design continuously and automatically rewards all users financially in IOTA for all of their data applied by the system towards adding value to the world. Effectively, VRENAR monetises the valuable data of all users and pays it to them directly.

Further information on the VRENAR Concept Design can be found from the main website and associated links there [18].

VRENAR is a non-profit project, offering all intended services not only for free to all users, but actually rewarding those users financially for their presence on the network, with alternative modes of work. It has no interest in user data for the purposes of making financial gains, other than those distributed to users.

Business Case

The overall business case of VRENAR leverages Metcalfe’s network effects to reward both new users of the VRENAR network, and existing IOTA token holders, by significantly boosting the value of the IOTA token relative to other currencies. Rewards paid to users in return for user data are similarly amplified by the same network effect. Thus individual data of virtually no value in isolation becomes a commodity of high value when processed in the distributed network. This is then monetised at the higher value and rewarded back to each contributor, enabling all users to be self-sufficient on the network.

The initial source of user funds paid by VRENAR to users is from bootstrap funding initially, followed by funds generated internally from user data deposited beneficially in the real world, as well as in a distributed virtual world AR/VR replica of the real world, in return for revenue reflecting the value added to all of those.

Document & Systems Engineering Methodology

Our approach is to search the available literature to evaluate the methods and relative successes of strategies used on other projects and networks, and to use that data and the lessons learned to underpin our own concept and method.

We employ 20 years of Chartered Engineer experience gained in large scale industrial and defence Systems in the application of state of the art Model Based Design, and ongoing academic PhD research, as part of a wider holistic Model Based Systems Engineering approach throughout our work on VRENAR.

Model Based Design (MBD)

We show the Matlab Simulink (TM) model built for the analysis and future control of the financial aspects of VRENAR. This illustrates also our technique of Model Based Design in action.

The current license for the Matlab toolset is graciously supplied to the author at reduced cost from Mathworks (TM) for carrying out the research necessary to complete the academic PhD project of the Remote-me sub-project[13] underway with the Open University, a core component of VRENAR. Raising sufficient funds for that activity, as by the activity of this article, in the absence of any other funds for the non-profit VRENAR or Remote-me, by way of showing how the tools are applied, is a necessary requirement for that activity, and is itself included as necessary researcher development skills evaluated towards the qualification of PhD [10].

As well as illustrating the power of the toolset in the conduction of projects such as VRENAR and Remote-me, as output by the selected tool of our Model Based Design approach, the Matlab Simulink (TM) model stands as an artifact capable of generating executable code, part of the initial VRENAR system prototype, which will be implemented as open source code maintained on Github.

Model Based Systems Engineering (MBSE)

We use a further Commercially licensed toolset; Sparx Enterprise Architect (TM) at a higher level in the holistic Model Based System Engineering of the VRENAR system, including the Remote-me project. This aspect of the System is expressed in the popular SysML/UML modelling language, including a framework in which the Matlab Simulink models are situated.

The SysML/UML System Model is variously executable, again capable of generating executable code, as already implemented as open source code on Github as part of the VRENAR system prototype, as well as the SysML/UML model itself.

We trust this information provides further confidence to investors of the project feasibility, and of our unique capability to carry out the work of the project.

Metcalfe’s Law

Our literature search finds only one reference to the description of an original document describing Metcalfe’s Law. This is cited by Metcalfe himself, as an article in the New York Times, 15 July, 1996, titled “There Oughta Be a Law”, in an IEEE article defending the law forty years later [15].

“There Oughta Be A Law”, Bob Metcalfe, The New York Times, 15 July, 1996

Metcalfe’s Law is also most conveniently described in Wikipedia [14].

In essence, it states that the value of a network is proportional to the number of users in the network squared. The first principles around this are based on the number of two way paths that exist from each user, to all of their peers in the network. The sum of this is given by N*(N-1), which converges towards N² for large numbers of users.

Thus the Metcalfe value function takes the form V=pN²

Metcalfe’s value function — The factor p.

The factor p is named the affinity factor in some texts, the virality factor in some others. This factor is directly related to the growth rate of the network, and the eventual maximum number of users in the network at the end of the network growth period.

Networks with a higher value of p experience greater growth rates.

As a measure of affinity, p can also be thought of as a measure of utility, or desirability of the network.

An approximate numerical value for p can be established by taking a series of known N vs V data points across the life of a network to date, and fitting a curve to it. This has been done in the case of bitcoin, as well as a number of other crypto-currencies [27].

In the case of a crypto-currency, assuming the currency value is not artificially inflated or depressed by market forces etc, we can obtain a reasonable value for p with a simple calculation of V/N², where V is the market value of the token, and N is the known number of network users.

Typical values for p for social media networks are much higher than for crypto-currency networks, for example. In fact, we note the case of social media to have one the highest known public network factors of p.

“Facebook creates much more value than is captured and monetized by Facebook selling ads”

— B. Metcalfe, 2103 [15]

To maximise the value of our intended network, we must give it at least all of the utility and desirability of a social media network.

It follows that by providing a network with more utility, such as ability enhancing AR/VR technology, machine learning algorithms in the network acting in the users interests, with significant financial rewards offering users new modes of work, as are all in the VRENAR concept design, then we are very likely to be breaking new ground with a new, higher value of p than any network previously seen.

Planning conservatively — the use of worst case values

Limits in scaleability as already encountered in blockchain based DLT solutions (Bitcoin, Ethereum, Q4 2017 to date), have resulted in users experiencing a drop in utility of those networks. Thus the value of p is negatively affected. Hence the subsequent price drops seen in the related token prices are actually expected by Metcalfe’s law.

The drops seen also in the price of IOTA over the same period, despite it having none of the same utility limitations, can be explained by market forces artificially pushing the price down, due to most investors painting the whole crypto-currency market as having the same problems. This is likely to be due to the lack of understanding amongst investors of how the IOTA Diametric Acyclic Graph (DAG), or “Tangle” technology [14] differs from, and compares with conventional Blockchain.

We have strong confidence that the price of IOTA is likely to be temporarily artificially depressed below that which should apply, according to the actual utility and the number of users in the network. It is highly likely to rebound after realisation of this by investors.

Nonetheless, in the case of VRENAR combined with IOTA, we use this probable artificially lowered value of p in our calculations, as it serves as closer to worst case, ensuring we are less likely to overestimate our longer term forecasts of financial performance.

The number of network users in IOTA is currently unknown, as many users may be using more than one address.

However, we do know the number of addresses in use, from summing the numbers of addresses listed in the statistics [5, 26]{Accessed 13:11, 10/02/2019}:

Total no. of addresses = 321326.

It is assumed that the proportion of addresses vs users will remain approximately constant throughout the lifetime of IOTA, thus is a reasonable substitute to consistently represent the growth of the network.

Network Value

We set the network value as the market capability of IOTA.

The Case for Combining the IOTA and VRENAR networks

In the case of VRENAR, the task is not to build a new crypto-currency network, but to build on an existing one, namely IOTA.

The choice of IOTA followed extensive research, including some ICO experimental experience with earlier crypto-currencies carried out over a period of around two and a half years, concluding that currently, IOTA is the only established existing crypto-currency solution that meets the VRENAR requirements of infinite scaleability, and feeless transactions.

Proving the financial viability of connecting two networks together presents some challenge. We see no prior examples of this in our literature search.

However we find papers on the successful retrospect application of Metcalfe’s law to social media and distributed ledger networks, with particular analysis and reference to lessons learned from incorrect attempts made to apply it in the planning of multiple proposed commercial networks in the lead up to the era.

Our research on the literature settles on three papers in particular as most relevant:

Paper [1]

“Tencent and Facebook Data Validate Metcalfe’s Law”

This is a comprehensive analysis of Facebook and Tencent data, gathered and analysed against Metcalfe’s law, to evaluate its effectiveness.

It is a robust defence of Metcalfe’s law in response to allegations of invalidity.

Since the data used is from actual network growths recorded in practice, we take those values established for the parameters used in the equations there as a good starting point in our own predictions.

Paper [2]

“Metcalfe’s law after 40 years of ethernet”

This is a further robust defence of Metcalfe’s law by Metcalfe himself, in a return to the study of it after 40 years, with further illustrations of how the law is applied.

Paper [3]

“Metcalfe’s law: Not so wrong after all”

This is an analysis of commercial factors not taken into account by allegations made against the validity of Metcalfe’s law, thus further defending and validating Metcalfe’s law.

Two points in particular catch our attention, with implications worthy of separate analysis outside the scope of this article. These serve to reinforce confidence in the fitness for purpose of the VRENAR Concept Design, and funding plan, Specifically [3]:

“Briscoe et al. make two related mistakes. For one, they reason in static terms and apparently fail to realise that interconnection alters the networks’ competitive positions and may, over time, very well impact their market shares. Second, Briscoe et al. mainly reason in aggregate terms, whereas the strategic implicatons are best analysed by looking at the utility of individual users and how this utility would be affected by interconnection.”


“In markets that are subject to network effects, size matters. Hence, networks can create value for their members and for themselves by opting for interoperability and, in this way, in effect turning two or more networks into one bigger network. However, intuition would dictate (1) that such interconnection is most likely to materialise when networks are roughly equal size (and thus have similar gains) and (2) that, in the other case, an established, dominant network has less reason to interconnect than a new, fledgeling competitor — unless the latter can compensate the former by means of so called side payments.”

In both the above quoted paragraphs, we see the importance of taking into account the commercial and strategic interests (driven by the needs of the primary stakeholders — the shareholders), which are present in networks designed to make profit.

The second quoted paragraph above, upon reading could look like bad news for VRENAR; It is the smaller network seeking connection with the larger of IOTA, and yet it also seeks funds from the larger. This might at first appear contradictory to the logic in the paragraph.

However, the passage refers to profit seeking networks, whereas both VRENAR and IOTA are non-profits. Neither network has shareholders or owners seeking to profit from users. Rather, both networks seek to reward users. In both cases, in the event of expansion, the net flow of wealth is not from users to network (or its owners), but from the network to the users, by increasing the value of the tokens held by the users.

This logic reverses the trend observed between networks designed for profit, from one of competition in the case of for-profits, to one of collaboration in the case of non-profits.

That passage, and all of the reasoning used in paper [3], together with all of the evidence in papers [1] and [2] proving the validity of Metcalfe’s law, does more than just destroy the allegations made against Metcalfe’s law, they actually serve as a body of compelling reverse proof evidence supporting the VRENAR non-profit business proposal.

By Metcalfe’s law, the main stakeholders (the users) of both of the non-profit networks, IOTA and VRENAR stand to gain by interconnecting, with the larger network gaining more than the smaller network, since the increase of value will manifest as a boost of the financial value of the tokens held internally.

Following the same logic, the natural flow of compensatory funds during expansion is from the larger network to the smaller, i.e. from the IOTA network to the VRENAR network, and by that interconnection, the combined value is increased.

Hence it is a natural scenario for VRENAR to be funded from the IOTA Eco fund, and it is most convenient to model the financial effects of this scenario as that which would result from a combination of the two networks, and to build the system directly from that approach.

Metcalfe’s law applied to combined Networks

For the reasons given earlier, the value of p which will apply to VRENAR is likely to be very different from that already known for IOTA, due to the difference in utility between the two networks.

We must model the Metcalfe value of the two networks connected together, throughout their combined lifetime.

By Metcalfe’s law, in the case of the new much smaller network of VRENAR with higher value of p, connected with the IOTA network with lower value of p, the new network of VRENAR will quickly expand vastly beyond the numbers already in IOTA, with the effect that the VRENAR network quickly becomes the much larger of the two. We need to be able to simulate the effect of this on the value of IOTA throughout.

We find no past examples of this in the literature, so we derive our combined network model from first principles.

Illustration of Combined Networks from Sparx Enterprise Architect toolset

Combined Network Model Derivation

The Combined Networks illustration shows the two way paths between the peers in two interconnected networks; a 5 member network shown in blue, and a four member network shown red. The inter-network paths, connecting the users between the two networks, are shown in purple.

The utility factor p in the value equation appears as a multiplier of each two way path seen by each user, to every other.

Since they are measures of utility, the p values of the two networks are additive. The resulting combined network has at least some, if not all of the utility of both, thus the combined value of p is higher than that applying to either or the other network in isolation.

There may be overlap in the utility of any two networks in general, but in the case of VRENAR and IOTA, we see and assume no significant overlap of utility. If IOTA is removed from the VRENAR concept design, VRENAR has virtually none of the utility of IOTA, and conversely IOTA has virtually none of the utility of VRENAR.

So we set the p value applying to each purple path as the sum of P1 and P2.

The number of purple paths is 2*N1*N2.

Our computation of the total combined network value is:

V = p1*N1²+2*N1*N2*(p1+p2)+p2*N2²;

We note a recent online press article reporting a new IOTA partnership with Paracosm, with VR functionality [19]. This might already be some way towards providing the utility of the virtual world proposed here. Whether or not this overlaps, or indeed complements the non-profit vision of VRENAR, as perhaps an ideal solution for the required virtual world element is unknown. Until further details of that become clear, the analysis of the proposed utility here is probably best considered independently. VRENAR is also always open to offering our unique mix of experience, research knowledge, skills, and mindset in any collaboration.

Netoid Formulation

Metcalfe’s general netoid function describing network population growth takes the form:

N = A/(1+exp(B*(t-t0)));

A is a multiplier coefficient, numerically equivalent to the eventual number of members in the network, and B is an exponential growth factor which sets the rate of growth of the network. The time at which the function starts has to be offset by choosing an appropriate value of t0, otherwise the function maximum rate of change occurs at t=0.

From paper [1], the Metcalfe netoid functions describing the number of users in each of the social media networks Facebook, and Tencent, are as follows:

  • Facebook N = 1.45e9/(1+exp(-0.77*(t-2010.56)));
  • Tencent N = 2.61e9/(1+exp(-0.3*(t-2013.8)));

To construct an initial forecast netoid function for VRENAR, we consider firstly what we want to achieve. We set our initial target market to be 5% of the size of that for Facebook. This seems like a moderate target for our new social media.

So we set our netoid multiplier as:

(1.45e9*5%) = 0.0725e9;

We look at the rate of adoption of facebook and recall that the utility of facebook remained largely the same throughout the period of its uptake. There was no significant change in the utility it offered to users during that period.

In the case of VRENAR, our utility will change during adoption. Ideally we would plan the phasing in of our functionality in stages of development, beginning with standard social media functionality similar to that of facebook (But with with user rewards from the beginning), progressing through supporting general wearables, consensus mechanisms and network machine intelligence, Remote-me, and finally the VRENAR wearables.

Predicting accurate values appropriate to each of those development stages in advance seems unrealistic, so we settle at this early stage on an initial value for the exponential growth rate coefficient as being that for facebook, adjusted slightly positively, to account for the added utility of user rewards which will be present in VRENAR from the outset.

Essentially, this factor is a measure of the desirability of the utility. Increasing its value results in a higher rate of adoption.

Reecognizing our need to compete in the current climate of commercial competition, this factor requires to be higher than that for facebook which currently dominates social media.

We believe a significantly higher value of p than is possible in any commercial network will be achieved by offering the utility of user funding, to the extent of eventually offering full financial sustainment of all users in VRENAR.

We think it likely most Facebook users would be tempted to switch to an alternative offering self funding. However we stay with our conservative estimate of capturing 5% of that market for the analysis here, as this appears adequate to obtain the bootstrap funding needed for VRENAR.

We set our exponential growth co-efficient as:

0.77(1+50%) = 1.155;

And the netoid function appears as:

N = 0.0725e9/(1+exp(-1.155*(t-2010.56)));

To visualise this together with the netoids of Facebook and Tencent, we adjust the time offset of each, so as to present them all appearing to begin around t=0.

A plot from the simulation is shown below:

Mathworks Simulink(TM) Plot of Tencent, Facebook, and forecasted VRENAR shown together

We can see our modest forecast of the VRENAR total number of users looks small compared with that of Tencent or Facebook, but it should be noted from the value of the netoid multiplier function that this is still 72.5 million users, which, when added to the IOTA network, represents an increase in size over the current number of users in the IOTA network by a factor of around 230.

Minimum acceptable income rate (MaiR)

A minimum acceptable income rate of around $15,000 per year might be close to that which most individuals would consider necessary for self sustainment. We use this as a rule of thumb for the analysis here.

To achieve this, an individual would need to be paid IOTA such that the accrued amount, at the rates applicable at the instant of donation, totals $15,000

Evaluating Human Information

We know that human information has value. In fact, we argue, value is exclusively created by this alone. It is defined by our likes and dislikes. Yet there appears no definition in the literature of a basic unit of it that might be monetised, or which itself could be considered a form of currency, directly convertible to disposable cash.

For the purposes of VRENAR (And perhaps also IOTA), we define a basic theoretically measurable unit of valuable human information, directly convertible to the units of our chosen cryptocurrency.

To make it something memorable, we look at the general meaning of IOTA, and see it defined as something infinitesimal [22], with an example quoted as:

“Did not show an iota of interest”

We see also in the Greek alphabet there [23], the symbol for IOTA is a lower case “i”. So we define our unit of human information as a human-IOTA, by prepending a lower case “h”, denoting “Human”. It follows that this notional human IOTA unit of information has a value equivalent to one IOTA.

One hi = One IOTA.

Further, we arbitrarily set the default information production rate of an average idle person as one hi per second.

Thus we are setting the default value of a person as one IOTA per second. We are unlikely to be able to accurately measure all aspects of that information such that it can always be completely captured, but we can probably get close, to within 80 or 90 percent overall.

For a person not idle, for example participating in consensus activities, placing a vote would be worth a number of hi, where that number reflects the complexity of the issue. Similarly, an evaluation, like an appreciation of an artwork would be worth a number of hi, calculated by a function of how long the appreciator spent admiring the article, and the usual time averaged amount of hi output by that user.

The detailed Evaluations Logic, of how this will be carried out will be elaborated in the System Concept Design as the project progresses.

Directly rewarding the user for the default value at the current price of IOTA equates to around 31 MIOTA per year. This equates to around $8 per year at today’s MIOTA price of about $0.24. However, the MIOTA price with VRENAR is forecast to hit $500, thus provide the minimum required income per user of $15,000 by around the end of the fourth year of the project.

In the six years after that, we see the forecasted MIOTA price continuing to rise beyond $50,000 per unit.

These figures do seem incredible. Hence the extended delay in releasing this document due to much closer examination of the whole analysis.

At the date of publication, trials with deep learning neural network controllers to moderate the scaling of user rewards, to preserve the long term initial market value of the bootstrap token fund whilst maximising rewards paid to all users, are underway. The selected form of 2D network will comprise the system economic Ai. In addition, each user will be allocated a personal 3D Ai, which will interface with the system Ai, measuring the user’s contributed human information, and rewarding the user for this.

We welcome all challenges to this information, to assist in identifying where mistakes might have been made in our assumptions, or other evaluations.

We propose to reward all users with the default rate of IOTA in lieu of human information measurement and evaluation systems development.

As time progresses on the project we expect to be able to firm up these definitions, but for the moment we trust they serve to get the project running.

This initial definition enables us to tie the value of the information from each individual user to the value of the community, since this is directly tied to the IOTA token. Thus, as the community value increases with increasing numbers of users in the network according to Metcalfe’s law, so also does the value of the information produced by each user, and every user has a powerful incentive to do what they can to maximise the network utility.

The hi unit must begin as a concept only, until later in the project when user information evaluation mechanisms comprising machine intelligence, combined with the crowd power of the users via consensus will be implemented. This which will help us define it further later, as necessary.

The virtual world used by VRENAR is the main repository of value. All artifacts there will be continually improved over time by a continuous process of user evaluations, coupled with machine intelligence, with the effect that continuous revenue may be obtainable through the provision of paid access to commercial entities wishing to make use of that data, at the discretion of, and under the control of the users both individually, and as a collective.

Rate of rewards control

It is fair to reward users with two forms of revenue, one from the user’s activity on the network, and the other representing the increase of value of the network, as the latter is also a fruit of the activity of users, working to increase the network utility factor.

Network Value Revenue

The Network funding capital value needs to be maintained such that the network is optimally funded throughout the lifetime of network expansion, with the end result that all funds are distributed throughout the network.

The aim of distributing the network value is to gradually transfer all of the network capital to users.

The simulations give our initial estimate of the network expansion to full adoption as between 10 and 20 years.

During that time, the network has three financial goals:

  1. Preservation and maintenance of the network capital asset (The grant capital), in order maintain maximum dividend yield throughout the period of accelerating network expansion.
  2. Payment of the network development and maintenance costs
  3. Distribution of the network dividends.

Acceleration and Deceleration Expansion Phases

This is further divided into two distinct phases; Acceleration, and Deceleration.

During acceleration, the slope of the network adoption curve dN/dt follows an upward trend. Approximately halfway through the network expansion phase, the rate of network expansion begins to decelerate. At that point, the slope of the second derivative, dN²/dt² passes through zero and goes negative, rising back up to near zero when the network has been fully adopted.

Network Dividends & Rewards Distribution

Different user rewards apply during acceleration and deceleration.

In acceleration, the user rewards comprise purely of dividends from the network capital appreciation. These are just shares in the value expansion which occurs in the network with additional users. Additional tokens will be bought using the increased value, and distributed to the network users, with a view to preserving or increasing the capital value. A further clearly defined portion of the appreciation interest will also be used for network development and maintenance funding.

In the deceleration phase, dividends will comprise both of value interest, and a fraction of the network capital. These combined funds will be progressively distributed across the network throughout the deceleration phase. This will be done in a way to gradually transfer the majority of the network capital to the users, with a view to completing at the same time as completion of network expansion.

The network value dividends comprises a share of the value increased over the original

In a network of p=0.01, going from 4 to 5 members:

dV/dN = 0.01*(5²-4²)/5 = 0.018

So a general case is p*(B²-A²)/B.

Substituting A = B-1;

dV/dN = p*(B²-(B-1)²)/B

For large numbers in the network, (B²-(B-1)²)/B tends to a value of two.

Thus dV/dN simply tends towards 2*p for large numbers in the network.

So for each member added, we reward a value proportional to p.

Increases in the value of p will result in greater rewards to each person in the network.


We set the initial value of the network as the USD value of the grant capital. according to the market rates applicable at the time of calculation.

For example, if the grant amount is one million MIOTA:

Currently, USD value of Grant @ $0.28/MIOTA [24]: $280,000

For robustness against currency fluctuations, the system value and economics are controlled in terms of gold rather than any particular currency.

Gold value of Grant @ $42.25/gram [24]: 6627.22g

We set this value as the initial starting value of the VRENAR system.

From this point, during acceleration we regulate the rewards distribution to maintain the initial capital stock value. Each person added to the network from that point theoretically enriches the system by the value of an additional amount of gold proportional to p, multiplied by the resultant number of users in the network.

In effect, everyone is paid from the interest accruing on the original invested capital.

Adaptive P

The actual utility of an initial network with relatively few members is very low. The network cannot become useful until at least a few hundred members have been added. Thus the network is likely to make some initial losses distributing funds to these users at any practical rate until the actual p value can be determined from analysis of the curves of actual MIOTA value vs numbers of users in the network.

Until then, we must artificially set an initial value of p at the smallest value practical to proceed with the development work of the network.

During acceleration, rewards need to be controlled such that the amount rewarded is maintained always at something less than 2*p, in order to maintain the maximum value in, (and thus maximise the rewards distributable from) the network capital.

Conversely, during the network deceleration of expansion, rewards need to be controlled to something greater than 2*p, so as to gradually distribute all of the network capital to the users, except for an amount needed to maintain the network.


Whilst dN/dt ≥ 0; We set the per user network reward < 2*p

and whilst dN/dt < 0; We set the per user network reward to > 2*p

We introduce a Reward rate variable R, to obtain a reward controlling factor in the form:

Reward = dN/dt*R*p

As explained earlier, p is likely to increase throughout the project, by an amount defined by the network economic Ai. The method of controlling R needs to be robust to this, as well as external market fluctuations.

The control algorithm monitors the market prices of both gold and IOTA, the number of addresses in IOTA, and the number of users in VRENAR, to control the value of R such that the long term market value of the IOTA bootstrap capital issued to VRENAR remains the same, whilst distributing all of the interest accruing on this (due to network expansion) equally amongst all of the users.

The control algorithm is implemented as a machine learning algorithm in the System economic model. This is initially trained [28], using historical data representative of the performance of IOTA to date. We have not yet found a source of historical data detailing the address build-up of IOTA. However, we did find a source giving the real time number of addresses [5]. By summing these daily and recording in a spreadsheet, we are able to confirm that the number of addresses is increasing daily, similarly to the early days of Bitcoin. Thus we see IOTA is indeed on the adoption curve.

We constructed a representative curve for IOTA using the known curve of Bitcoin prior to the scaling issues encountered in Bitcoin as mentioned earlier. We use Bitcoin rather than Ethereum, as the latter has smart contracts functionality which is not in IOTA as yet.

We note that whilst IOTA has many IOT applications under development which are additional to any functionality offered by Bitcoin or Ethereum, IOT as yet is a fairly specialised interest compared with the interests of most general users. Most are probably just interested in a simple crypto-currency. This also is indicated by the market continuing to drive the price of IOTA downwards over the past year, despite increasing numbers of adoption, we deduce that the p value of IOTA is not much stronger than that of Bitcoin in the time before its scaling issues.

So it seems reasonable to assume that the growth curve of IOTA will follow a similar trajectory as that experienced by Bitcoin, with the exception that IOTA will continue on past the point where Bitcoin hit the scaleability wall. Continuing along that curve [27], the mean price of bitcoin if it had not hit the problem of scaleability limitation, would be around $35,000 per token today.

This is not a bad future for IOTA. However, for the reasons argued earlier, we believe it will be vastly improved by incorporating the high utility of VRENAR in the network.


We have concentrated on a theme of utility in the context of network growth throughout our analysis. We show that this can be maximised in a way only possible by non-profit operating, and that this is key to achieving network growth unlike any seen previously. VRENAR itself mates the technologies of VR and AR by way of integration with a distributed virtual world, in addition to user oriented machine intelligence, so as to enable new use cases and modes of work which have never been possible previously.

We can see that maximising utility is the key to maximising the rate and extent of uptake. If the uptake is massive, then the benefit per user is significant.

Suggested Further Research for all Interested Parties

  • Further study needed to further define hi, the unit of human information with methods of elicitation, capture and verification of this.
  • Study on analysis of the Metcalfe utility factor p in terms of Use Cases (We suspect a linear relationship exists to the number of fully decomposed Use Cases). This could possibly be used as part of an evaluation mechanism to calculate rewards payable for creation of new functionality in the system.


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  2. Metcalfe, B. (2013) ‘Metcalfe’s law after 40 years of ethernet’, IEEE Computer Magazine, pp. 26–31. doi: 10.1109/MC.2013.374.
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  13. Bott, F. E. (2017) ‘Abstract: The Possibilities of Real World First Person View ( FPV ) Unmanned Aerial Vehicle ( UAV ) Interactions with the users of Virtual Environments’, Proceedings of the Open University CRC PhD Research Conference 2017, (2), p. 2.
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  26. Spreadsheet on Github used to manually record IOTA number of addresses growth
  27. Alabi, K. (2017) ‘Digital blockchain networks appear to be following Metcalfe’s Law’, Electronic Commerce Research and Applications. Elsevier B.V., 24, pp. 23–29. doi: 10.1016/j.elerap.2017.06.003.
  29. This is not a reference, rather, a point of interest


  1. This document is a work in progress at the original time of publication. The materials in it may change, including all references to IOTA, if it becomes apparent that the project is more suited to a different token (i.e. if the project receives support from another suitable token community before significant support can be elicited from IOTA).


Source: Artificial Intelligence on Medium

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