Neutrosophy as a tool to navigate a hybrid convex-concave world
By Dr. Ranulfo Paiva Sobrinho & M.A. Karla Córdoba-Brenes
Introduction
“…the world is not entirely convex, but it is not entirely concave either. But the existence of some concave path between any two distant positions A and B is very likely, and if you can find that path then you can often find a synthesis between the two positions that is better than both…” — Vitalik Buterin
This quote was the conclusion of an interesting blog post entitled “Convex and Concave Dispositions”, by Vitalik Buterin, Ethereum cofounder. According to Vitalik, if there is the possibility of finding a synthesis between two positions, this synthesis could be better than both of those positions.
As we navigate the complex world in which we live, finding a synthesis that is better than both positions may be desirable in one specific context, but in other contexts it may not. Even if it all depends on the context, Vitalik gravitates towards finding a synthesis, or a more concave approach, and so do we.
This way of seeing the world is essential if we are to have a less polarized society, or if we aim to find solutions to complex problems that consider the good things of proponents who differ on ideologies, or positions towards a subject. Reflecting on this, we consider that what could improve decision-making is being able to see and express a spectrum of opinions, instead of only extremes or middle points.
We believe that Neutrosophy can help us find the mentioned synthesis when such synthesis is possible. As we will show in this post, since Neutrosophy goes beyond polarizing logic it also has the potential to improve decentralized governance systems, like those applied to DAOs or collaborative businesses.
The purpose of this text is to introduce Neutrosophy as a tool to help us navigate a hybrid multidimensional convex-concave world. By navigating we mean making better decisions and/or expressing our opinions in the complex, messy contexts that sometimes we face.
It also briefly introduces NeutrosophyLib, a Solidity library containing basic neutrosophic operations for those interested in exploring these ideas.
Beyond polarizing logic
For centuries, the reasoning of many human beings has been influenced by polarizing mathematical logic. Such logic induces people to categorize things as follows: a thing can belong, or not belong to a set. But what happens if you are not sure? If that belonging or not belonging is not clear to you? This logic does not allow you, an individual or a group, to express the level of indeterminacy, or the level of “I don’t know if that thing belongs or doesn’t belong…”.
Boolean logic is an example of polarizing logic that categorizes things using a membership function with two values: one or zero. If something belongs to a set, the membership function value is equal to one, otherwise, it is equal to zero.
The ‘convex world’ is characterized by polarized actions, statements, or proposals, that illustrate the case of Boolean logic. In the quoted blog post, Buterin mentioned a statement from the Bitcoin land:
“…any system must have either a fundamentally centralizing or a fundamentally decentralizing tendency, with no possibility halfway in between…”
Regarding this statement, we think that in certain contexts it could be valid. However, by observing the evolution of the crypto space since 2009 and as cofounders of initiatives using blockchain for environmental and social impact such as Cambiatus and Cofiblocks, we are confident to say that we can have a system that has not a 100% centralizing tendency, or has not a 100% decentralizing tendency, but could have characteristics of both (at the same time or over time).
We observe the influence of polarizing logic also in the Ethereum ecosystem, such as in DAO’s governance voting process. This is the case with the Governor’s smart contract.
The Governor contract via the contract castVote gives voters the following options to express their opinion about a proposal:
(a) For (it means, I vote for the proposal)
(b) Against (it means, I vote against the proposal), and
(c) Abstain (it could be interpreted as I choose to not express my opinion regarding the proposal). See Figure 1 below.
Due to Boolean logic, which assumes only two values or options, a vote casted using castVote could be interpreted as: whoever voted ‘For’ or ‘Against’ the proposal is either 100% in agreement or in disagreement with it.
But in real life, a voter could agree with the proposal partially and have doubts and disagree with certain parts of it. These nuances are lost when someone uses polarizing logic to structure a voting system.
Fortunately, these nuances are intentionally and explicitly incorporated in a voting system when using more modern and advanced mathematics such as Neutrosophy.
Figure 2a represents a general voting framework based on Neutrosophy. You can see in Figure 2b an example of what would be the result of a person voting based on Neutrosophy. In this case, the person can express how much it agrees (For), and, how much it is (Undecided), and how much it disagrees with the proposal (Against).
The nuances previously mentioned are explicit when using Neutrosophy and could help us make decisions in hybrid convex-concave contexts.
Now, let’s understand the basics of Neutrosophy.
Neutrosophy
Neutrosophy is a branch of Philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra, considering a proposition, theory, concept, event, or entity A in relation to its opposite antA, and that which is neither A nor antA, denoted by neutA [1].
Neutrosophy allows a person, or group to express an opinion about something in a way that recognizes:
(a) in what parts there is an agreement (A), as well as
(b) where it remains neutral, or undecided, due to a lack of information (neutA), and
(c) the parts on which there is disagreement (antA).
The mentioned entity ‘A’, its opposite ‘antA’, and ‘neutA’, constitute the core elements of Neutrosophy. Depending on the context in which we apply Neutrosophy, its elements can assume different names, as shown below.
Different names to represent Neutrosophy elements =
· { For, Undecided, Against }
· { Convex, is not entirely convex but it is not entirely concave, Concave }
· { A, neither A nor antA, antA } = { A, neutA, antA }
· { True membership function, Indeterminacy membership function, False membership function }
· { Good, Neither Good or Neither Bad, Bad }
· { the degree of Truth (T), the degree of Indeterminacy (I), and the degree of Falseness (F) } = { T, I, F }
The degree of Indeterminacy (I) is independent of the other two. We will adopt { T, I, F } as a general representation of neutrosophic elements.
Single-Valued Neutrosophic Number (SVNN) and Set (SVNS)
In Neutrosophy there is something called a Single-Valued Neutrosophic Set (SVNS) as proposed by [2]. The SVNS was created to apply Neutrosophy to solve problems and develop applications in real-life.
A SVNS can be empty or can contain numbers called Single-Valued Neutrosophic Numbers (SVNN).
In a SVNN each Neutrosophic element {T, I, F} can have a numerical value ranging from 0 up to 1, meaning that the sum of the three components lies in a range between 0 and 3.
A SVNN can be represented as follows:
Enough theory! Let’s see a real application for those who love good coffee, as we do.
Voting System Using SVNS: CofiBlocks case
We are developing a voting system for CofiBlocks based on Neutrosophy using NeutrosophyLib (Solidity library). We are in the early stages. CofiBlocks is a Web3 initiative supported by Satisfied Vagabonds[8] and Cambiatus[6] to help coffee small farmers in Costa Rica. We intend to solve this problem:
“… For every cup of coffee sold for $3, the coffee producer receives $0.03. If this amount could be doubled, it would have no negative effect on the consumer but would be a life-changer for the producers…”[3]
In short, CofiBlocks, small coffee producers, coffee lovers (consumers), and coffee supporters can interact, make decisions, and share responsibilities and benefits. If the business activity generates profits, 30% belongs to coffee producers, 30% to coffee lovers, and the remaining to Cofiblocks and its supporters. All members learn to use Web3 tools and how to make decisions using Neutrosophy and other tools.
The mentioned voters (Helia, Marco, and Joana) will vote on a proposal presented by another member, Omar. The hypothetical proposal is:
“We should include three gourmet coffees from Costa Rica to export to USA and Europe.”
As noted in Figure 3, the three voters (Helia, Marco, and Joana) have practically no objection to the proposal. Helia is more in favor of the proposal and has less indecision regarding it. Probably, she talked more with Omar and knows the proposal details. But Marco and Joana have a high degree of doubt and less level of agreement regarding the proposal. Probably they need more details regarding the proposal.
In a governance process using Neutrosophy, the group could decide that certain conditions must be attended to for certain types of proposals to be approved.
These are three hypothetical conditions to illustrate this point:
· the level of agreement must be greater than 0.7; and,
· the level of indecision must be below 0.4; and,
· the level of disagreement must be less than 0.5.
If we adopted these conditions to analyze the results in Figure 3, Omar’s proposal should not be approved, because Marco and Joana expressed a high level of indecision and a low level of agreement. In this case, the system should notify Omar and inform him that he needs to clarify his proposal and present it to be voted on again.
This process could occur offline and be repeated a maximum number of times (each organization should decide how many).
Can Neutrosophy help us improve governance in DAOs or collaborative businesses?
We believe the answer depends on the context. If a community faces situations where Neutrosophy could help and its members are open-minded to explore it, so the answer is yes. If you and your cofounders are starting a new community and want to explore new possibilities beyond the polarizing voting system, the answer is yes too.
In our case, we are developing a governance system for CofiBlocks using Neutrosophy (still early stage). We intend to go deeper and explore new possibilities beyond the voting system.
We believe that using Neutrosophy opens new opportunities. Once we acquire the Neutrosophic mindset, we can use it to imagine, and co-create new decentralized governance systems.
We want to explore the possibilities that Neutrosophy offers and share them with the Web3 community.
NeutrosophyLib
Using Neutrosophy to support decentralized governance implies a mindset change. Using an analogy, it is like changing our vision in a way that instead of black and white (B/W), we now can see a gradient, a grayscale that deepens our vision, allowing us to see volume and more natural and rich shapes. We see more details.
Adopting Neutrosophy implies allowing each person to express, respectively, his/her degree of agreement, indecision, and opposition with respect to something (Figure 3). In doing so, we need to use different mathematical operations to process the inputs and generate the outputs.
NeutrosophyLib is a Solidity library, created by the first author of this article (Ranulfo Paiva Sobrinho), to introduce basic neutrosophic operations developers can use. The NeutrosophyLib manual gives you details regarding neutrosophic operations. We are prototyping applications and will share them soon.
Find here the NeutrosophyLib repository on GitHub
Important note
The first author is not a professional developer, so developers, please, be patient in reading the code. And feel free to improve it.
Would like to support us?
If you like these ideas and want to support them, you can in several ways:
- Explore, join and share other initiatives by Satisfied Vagabonds.
- Send us some ETH!
Our gratitude
To Patrick Collins and Cromewar for sharing with the community so valuable learnings regarding DAO Governance, and smart contract development[4]. To Vitalik Buterin for sharing your provocative visions regarding DAO Governance in your blog posts[5]. We also thank Cambiatus[6] team members for embracing Neutrosophy math as a useful tool for decentralized governance during our Cambiatus learning sessions. I also thank ReFi Costa Rica and ReFiDAO [7] for hearing about the Neutrosophic ideas and being open to using them in the development of new financial instruments aligned with life (in progress).
References
[1] Smarandache, F. 1999. A unifying field in Logics: Neutrosophic Logic. In Philosophy. American Research Press, 1–141.
[2] Wang, H.; Smarandache, F.; Zhang, Y.; and Sunderraman, R. 2010. Single valued SVNS sets, Multisp Multistruct 4: 410–413.
[3] Cedeño, A., G.A. Jiménez, L.D. Gené. 2020. Estudio exploratorio sobre innovaciones tecnológicas aplicadas al sector café y cacao. América Latina. Nación Regenerativa.
[4] https://www.youtube.com/@PatrickAlphaC
[5] https://vitalik.ca/general/2020/11/08/concave.html
