Degree of Separation

5 Min read

Social connection on Earth in 2023

Network theory

U.S. Army and Armed Forces

Math geek special, logarithm





Thought exercise for the day. How many friends between you and anyone on the planet?

In popular culture this number is often referred to as Six Degrees of Separation*, that all people on the planet are at the maximum six or fewer social connections away from each other. The idea likely originated in a 1929 short story and became notable in 1990 in John Guare’s play of the same name Six Degrees of Separation.

I’ve been thinking of the small world idea–which is a theory by the way–after a visit to a military event in Nashville. Certainly this degree of separation is a smaller number in the Army. It seems to be only 1 or 2 degrees of separation, as a practical matter based on a lifetime of anecdotal evidence. And without delving too far into the math weeds, that would make sense since the U.S. Army is roughly 500,000 active duty and 1.3 million active armed forces, all branches.

A theorist suggested that this degree is simply the logarithm of the size of the population. As a simple example, here are some degrees of separation.


World population of 8 billion, average number of acquaintances, say 30 people. The base 30 logarithm of 8000000000 is 6.704317574 or how’s that for validation of the current planet population, we are separated by 6 to 7 people from every other person on the planet! Stick with me now, don’t worry about big numbers, but read on, because it makes sense.

Let’s say the number 30 represents close connections and we can actually have 300 meaningful acquaintances, and 3000 people we recognize, call that the handshake connection. Yes, that was a theory or experiment. The base 300 logarithm of 8000000000 is 3.9978220558, so if we know 300 people, we are 4 social connections away from anyone else. And for the handshake connection, the base 3000 logarithm of 8000000000 is 2.8480715113, or 3 people away.


Naturally, I had to go back to my Army idea and check for degree of separation for roughly 500,000 troops. With 30 close connections the degree of separation is 3.858; with 300 meaningful connections the degree is 2.3 and for the busy nodes in the network who have 3000 connections the degree is, get ready — did you guess, 1.6! So yes, in the current US Army then, we are separated by 1 to 2 friends or social connections. In the world at large, we are 3 to 6 away from each other.

When I read Thich Nhat Hanh’s advice to show kindness to everyone and in every engagement with others to exhibit compassion, then I realize what he achieved in a lifetime of nearly a 100 years and writing over 100 books. Admiral McRaven made the same argument in the opening of his now viral commencement speech.


I leave you with one last thought. Read this excerpt and consider the impact that you have in every single interaction, every day, with every person you meet.


So acknowledging that fact, if I can’t make this commencement speech memorable, I’ll at least try to make it short. So the university slogan is, what starts here changes the world. Well, I’ve got to admit, I kind of like it. What starts here changes the world. Tonight there are almost 8,000 students or there are more than 8,000 students graduated from UT. So that great Paragon of analytical rigor says that the average American will meet 10,000 people in their lifetime. 10,000 people, that’s a lot of folks. But if every one of you change the lives of just 10 people and each one of those people change the lives of another 10 people and another 10 then in five generations, 125 years, the class of 2014 will have changed the lives of 800 million people, 800 million people. [Full Transcript, UT Austin speech 2014, 59 seconds, William McRaven]



*Fun with logarithms. Visit this site to try your own calculations based on your number of friends and population size. (Rapidtablescom)

*Six Degrees of Separation – such a fun topic to explore especially with social networks today facilitating readily available data on users and friends, interactions, etc. Twitter data suggests that users are 3 to 4 steps away from each other.

Users on Twitter can follow other users creating a network. According to a 2010 study of 5.2 billion such relationships by social media monitoring firm Sysomos, the average distance on Twitter is 4.67. On average, about 50% of people on Twitter are only four steps away from each other, while nearly everyone is five steps or less away.[41]

In another work, researchers have shown that the average distance of 1,500 random users in Twitter is 3.435. They calculated the distance between each pair of users using all the active users in Twitter.[42]

*Admiral McRaven’s math on human reach in his commencement speech. Excerpt below from Dutch teacher.

The Admiral used his own math formula, which was something like this:

Did they know that they possessed the power to touch nearly 800 million people over the next 125 years?

Total # of people present TIMES # of people reached (20) TIMES five generations (grandparents, current, plus the next three = 125 years) TIMES 10 (factoring in 10 more lifetime interactions from everyone in the original total).

Complicated mathematical equation

When I used this formula to calculate the collective impact on the world for the 2014-2015 school year based on my own school district’s numbers (Holland, MI), I couldn’t believe it.

The combined world influence and reach by just Holland’s teachers alone for the upcoming school year exceeds 7.8 MILLION persons.

**For kicks and grins, if you thought of Kevin Bacon as I did, your memory serves you well. Here are the wiki notes on that.

Kevin Bacon game[edit]

The game “Six Degrees of Kevin Bacon[23] was invented as a play on the concept: the goal is to link any actor to Kevin Bacon through no more than six connections, whereby two actors are connected if they have appeared in a movie or commercial together. It was created by three students at Albright College in Pennsylvania,[24] who came up with the concept while watching Footloose. On September 13, 2012, Google made it possible to search for any given actor’s “Bacon Number” through its search engine.[25]

Upon the arrival of the 4G mobile network in the United Kingdom, Kevin Bacon appears in several commercials for the EE Network in which he links himself to several well known celebrities and TV shows in the UK.

Jun 10, 2023


About the Author

Mylinh Shattan is a writer who has lived on three continents, served in the Army, worked in corporate America, and taught in college. She loves adventures, in the world and in the mind. Literature is relevant and learning is a lifelong pursuit, so you might as well have a bit of fun along the way.

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