On page 306 of Scale, Geoffrey West discusses Dunbar’s Law and its implication for human social networks. To summarize this law: it claims that humans have multiple levels of bonding strength. At the lowest level a human will have around five connections of the strongest type of friendship and intimacy. Typically this would include some members of one’s family or a best friend. At the next level there are around fifteen connections that are not as strong as the first level, but are still firm. This would include close friends you might talk to on a daily or weekly basis. At the next level there are about fifty connections… and so on… The numbers of connections scales by tripling the connections at each higher level. In the book the levels are labeled as: 1) Kin, 2) Super-family 3) Clan, 4) Tribe, and 5) Strangers.

When I first read this in Scale, I was immediately reminded of David Graeber’s anthropological work regarding economic relationships among humans. In his book Debt: The First 5,000 Years, Graeber observes on page 99-100 that baseline communism (sharing) follows a similar structure. Thus, using the terminology from above: At the kin level Graeber notes that there is much sharing between members and the relationship is baseline communism. Thus, you can extend this and map these economic relationships with those of Dunbar’s Law: 1) Kin (~5 people) : Almost all sharing with very little debt or IOU, 2) Super-family (~15 people) : IOU with a good amount of sharing, 3) Clan (~ 50 people) : Mostly IOU and little sharing, and 4) Tribe (~150 people) : Almost entirely IOU with very little sharing. Anything outside the tribe would be exchange via a cash medium except in rare occasions, such as a child falling in front of an on-coming vehicle (a person would naturally share his strength to save the child’s life). Although I may not have followed Graeber’s observations exactly I find this train of thought to be interesting as it requires one to rethink the concept of currency, exchange, and economic relationships. Indeed, Graeber’s book challenges the entire paradigm of the historical development of currency and debt by analyzing the anthropological record.

I first ran across Hidden Forces while listening to the interview with Ray Monk about philosophical mathematics. Monk’s narration on the work of Frege, Russell, Whitehead, Wittgenstein, and Gödel is excellent – by far one of the clearest and easiest to grasp. It was learning about these paradigms and paradoxes of mathematics via Hofstadter’s famous book which led me to start this website.

Warren: I know a great idea!

Ben: Sure, tell us another one of your “great” ideas. I hope this one is better than that silly farming device.

David: Alright, let Warren indulge us.

Warren: Ok… so, what if we printed pieces of paper and told people that they were worth the value of a certain company?

Taylor: Is that your idea? Hahahaha, what could that possibly achieve? I am leaving.

Warren: No, wait! Just think about it. If we printed a fixed number of these papers and said that the sum of the them are worth the value of the company, then we could sell them for that value to people.

Ben: Yes, but what fool would fall for such an obvious scam.

Taylor: What value? How can pieces of paper be worth more than paper? How can we claim that they are worth the value of a certain company?

David: You know, I think Warren has a point. All we have to do is sound reputable and create a way for these pieces of paper to be traded.

Warren: See! David is following me!

David: If this were a scam, we would just sell the papers and run off with the money.

Ben: But isn’t that your plan?

Warren: Hmm… True. But in this case, the people are able to trade with each other to get their money back and possibly a profit.

Ben: In fact the potential for a profit would be the only reason for buying these pieces of paper.

Taylor: Hahahah, so this is a giant Ponzi Scheme?

David: Yes, it does seem so, now that you mention it.

Warren: No, there is a difference. We will simply be selling pieces of paper. The “Ponzi Scheme” that Taylor mentioned would be caused by the infinite self-repeating pattern of people buying the paper from each other and then selling it to other people for a return.

David: That is a very strange concept. Kinda like a strange loop.

Ben: Ok, but wouldn’t each person value the pieces of paper differently, based on their opinion on the value of the company?

Taylor: Yes, person Expensive may be willing to pay ten the piece of paper; while person Cheap may only pay ten for the same piece of paper.

David: Then this is idea is doomed. It will never work.

Ben: Too much chaos!

Warren: No! Someone, perhaps seeing an opportunity to profit will establish a definite lower bound to the value of the piece of paper. Let’s say that lower bound is ten; i.e., there is a person who believes that he can buy a piece of paper for ten and, at a later date, sell it to people for more than ten.

David: Ok. I follow.

Warren: Then, someone else, seeing that there is a potential to make money, will offer 12 for the piece of paper.

Ben: AHH! Yes, a price will dynamically form based on the interactions of all these people.

Taylor: And then?!?!

Warren: Well, then we have a way to sell these pieces of paper for more than the value of paper?

Ben: Yes, precisely.

David: So, by simply saying we have pieces of paper which represent the value of a company we have made a handsome profit?

Warren: Exactly!

Ben: And, in the process we have discovered a way to find the value of a company!

Taylor: Wow! I must say Warren, this is a brilliant idea!

David: What will we do will all this money?

Warren: I think I will buy some of these pieces of paper.

Ben: Me too! And make even more money!