Social Scalability

Source: Unenumerated <Nick Szabo blog>, Feb 2017

the secret to Bitcoin’s success is that its prolific resource consumption and poor computational scalability is buying something even more valuable: social scalability.

Social scalability is the ability of an institution –- a relationship or shared endeavor, in which multiple people repeatedly participate, and featuring customs, rules, or other features which constrain or motivate participants’ behaviors — to overcome shortcomings in human minds and in the motivating or constraining aspects of said institution that limit who or how many can successfully participate.

Social scalability is about the ways and extents to which participants can think about and respond to institutions and fellow participants as the variety and numbers of participants in those institutions or relationships grow. It’s about human limitations, not about technological limitations or physical resource constraints.

Even though social scalability is about the cognitive limitations and behavior tendencies of minds, not about the physical resource limitations of machines, it makes eminent sense, and indeed is often crucial, to think and talk about the social scalability of a technology that facilitates an institution.

The social scalability of an institutional technology depends on how that technology constrains or motivates participation in that institution, including protection of participants and the institution itself from harmful participation or attack. One way to estimate the social scalability of an institutional technology is by the number of people who can beneficially participate in the institution.

Another way to estimate social scalability is by the extra benefits and harms an institution bestows or imposes on participants, before, for cognitive or behavioral reasons, the expected costs and other harms of participating in an institution grow faster than its benefits.

The cultural and jurisdictional diversity of people who can beneficially participate in an institution is also often important, especially in the global Internet context. The more an institution depends on local laws, customs, or language, the less socially scalable it is.

Without institutional and technological innovations of the past, participation in shared human endeavors would usually be limited to at most about 150 people – the famous “Dunbar number”. In the Internet era, new innovations continue to scale our social capabilities.

Innovations in social scalability involve institutional and technological improvements that move function from mind to paper or mind to machine, lowering cognitive costs while increasing the value of information flowing between minds, reducing vulnerability, and/or searching for and discovering new and mutually beneficial participants.

Alfred North Whitehead said, “It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them.”

Friedrich Hayek added: “We make constant use of formulas, symbols, and rules whose meaning we do not understand and through the use of which we avail ourselves of the assistance of knowledge which individually we do not possess. We have developed these practices and institutions by building upon habits and institutions which have proved successful in their own sphere and which have in turn become the foundation of the civilization we have built up.”

Singapore: Tokens as Non-Securities

Source: FinRazor, Sep 2018

a representative of the Monetary Authority of Singapore (MAS) has spoken that the central bank has not yet considered any token as securities.

So far Singapore’s central bank perceived none of the tokens they considered are qualified to be regulated under its securities law.

Pang discussed the guidelines in A Guide to Digital Token Offerings which was published by MAS in 2017. In the guidelines tokens were categorized into three separate types:

  • Utility Tokens — are mined solely for accessing particular services provided by the company. MAS has no intention to regulate this token type.
  • Payment Tokens — can be used as a means of payment and holds value. By the end of 2018, a payments bill will be made into law.
  • Security Tokens — possess a promise or rights to a company’s future earnings.

Related Resource: Coindesk, Sep 2018


John Conway (Group Theory & “Game of Life”) Best Wishes

Princeton Emeritus mathematician Professor John Conway sends his best wishes

Professor Conway created the Game of Life cellular automata, which is Turing-Complete (similar to Ethereum).

cellular automata, as they appear in the Game of Life, have the same computational capacity as Turing machines. The Church-Turing thesis that states:

“No method of computation carried out by a mechanical process can be more powerful than a Turing machine.”

Therefore, as the Game of Life is Turing complete, it is one of the most powerful models of computation. In other words, no mechanical form of computation can solve a problem that a Turing machine or cellular automata cannot solve, given sufficient time and space. The following reasons lead researchers to determine the Game of Life has all the computational capability of Turing Machines, meaning it is Turing complete:

CA are computational systems: they can compute functions and solve algorithmic problems. Despite functioning in a different way from traditional, Turing machine-like devices, CA with suitable rules can emulate a universal Turing machine (see entry), and therefore compute, given Turing’s thesis (see entry on Church-Turing thesis), anything computable.

unlike Turing machines and von Neumann-architecture conventional computers, CA compute in a parallel, distributed fashion.

Using CA for Cryptography

Cellular automata yield a surprisingly diverse range of practical applications. We focus here on one particular example of a real-life application of cellular automata – the design of a public-key cryptosystem.

A public-key cryptosystem is a cryptographic protocol that relies on two keys – an enciphering key E, which is made public, and a deciphering key D, which is kept private. Such a system should contain two important properties:

1) Security. For attackers who have no access to the private key, the protocol should be so designed such that it would take a prohibitively large amount of time to recover the plain text from the cipher text.

2) Signature. The receiver should be able to tell who the sender is. In other words, if person A, say Alice, wants to send a message, she should be able to sign her message in a way that nobody but she could.

Public-Key Crypotography.

In the system, each piece of plain text consists of binary digit blocks of a certain length, say N. In turn, each set of, for example, k bits in the block can be viewed as an element of some ground set S. For instance, we can have a cryptosystem where each block contained 5 bits and each bit takes a value in a field of 2 elements.

Suppose now each block contains N bits and represents m elements of S. To satisfy the security requirement, we require an invertible function which maps Sm to Sm that satisfies the following conditions:

a) Easy to compute (for enciphering)

b) Hard to obtain its inverse without certain key pieces of information which only the receiver has access to (deterring would-be attackers)

The complexity of cellular automata lends itself nicely to applications in cryptography. In particular, cellular automaton rules that are invertible are prime candidates for the invertible function we require to construct a public-key cryptosystem. To succinctly represent the rules whilst preserving a large neighborhood-size, we can associate the ground set S with a mathematical structure such as a field or a ring. This way, addition and multiplication are well defined on S, and we can thus represent cellular automaton rules as polynomial functions.

Here is a sketch of how a cellular automaton cryptosystem might work. Let the ground set be a field. The enciphering key, E, is a composition of inhomogeneous and time-varying linear invertible rules which is made public (the observant reader might note that the fact that the rules are inhomogeneous and time-varying distinguishes the resulting cellular automaton from elementary cellular automata). The deciphering key, D, is the set of individual rules in the composite enciphering function.

The crucial factor that enables such a cellular automaton cryptosystem to work is the fact that it is extremely computationally expensive to unravel the original state from the cipher state without prior knowledge of the individual rules used in the composite enciphering function. This guarantees the security of the system.

Signing a message in our cryptosystem works in exactly the same way as signing a message in the RSA cryptosystem. All the sender has to do is to apply the secret decryption key D to her name and then include that coded signature at the end of her message. This way, when the receiver receives the message, he can simply use the public key E to decipher the coded signature and see if the name matches the presumed sender.


Gosper Gliding Gun



Game of Life on the Surface of Trefoil Knot

Red glider on the square lattice with periodic boundary conditions.

a 48-step oscillator along with a 2-step oscillator and a 4-step oscillator from a 2-D hexagonal Game of Life (rule H:B2/S34)