I agree with all of your thoughts here, and want to remark in support of the intuitions.
There’s a classic math question known as the handshake problem, which asks and answers things like: in a group of n people, how many unique handshakes can take place if each person shakes the hand of all the other n-1 people? If n=1, there’s only one person and they can’t shake anyone else’s hand, so 0 handshakes take place. If n=2, the second person can shake the first person’s hand, so there’s 1 handshake. If n=3, the third person shakes hands with each of the first two people, who also shake hands with each other. In general, the solution for n people is (n-1) + (n-2) + … + 2 + 1 + 0 = n*(n-1)/2. The most important insight or takeaway is that this expression is proportional to the square of the number of people, so the number of handshakes grows quadratically as more people are added.
I think fellowships strongly experience this effect, where adding one more participant to a small group will let that person meet the others in the group and provide a valuable connection to those few people, but adding one more participant to a large group provides a potential valuable connection to a lot more people. Going from 30 participants to 31 has a lot more potential upside than going from 20 participants to 21.
(These effects don’t continue forever, because there are different limiting factors that become relevant. Adding one attendee to a 1500-person conference doesn’t quadratically increase the value of the conference because the first 1500 people are already limited by the number of 1-on-1s they have time for during the event. And you can’t just change the fellowship from 30 people to 60 and expect it to be 4x as good; at that point, you’re going to start needing more space and everyone is going to be far from some of the other people, so there’s an asymptotic bound to the value that is less than quadratic.)
(Robi mentioned this to me in person; I thought it was insightful/asked him to comment.) Thank you for the insight Robi! This is an interesting way of thinking about my numbers claim that I had not considered.
I agree with all of your thoughts here, and want to remark in support of the intuitions.
There’s a classic math question known as the handshake problem, which asks and answers things like: in a group of n people, how many unique handshakes can take place if each person shakes the hand of all the other n-1 people? If n=1, there’s only one person and they can’t shake anyone else’s hand, so 0 handshakes take place. If n=2, the second person can shake the first person’s hand, so there’s 1 handshake. If n=3, the third person shakes hands with each of the first two people, who also shake hands with each other. In general, the solution for n people is (n-1) + (n-2) + … + 2 + 1 + 0 = n*(n-1)/2. The most important insight or takeaway is that this expression is proportional to the square of the number of people, so the number of handshakes grows quadratically as more people are added.
I think fellowships strongly experience this effect, where adding one more participant to a small group will let that person meet the others in the group and provide a valuable connection to those few people, but adding one more participant to a large group provides a potential valuable connection to a lot more people. Going from 30 participants to 31 has a lot more potential upside than going from 20 participants to 21.
(These effects don’t continue forever, because there are different limiting factors that become relevant. Adding one attendee to a 1500-person conference doesn’t quadratically increase the value of the conference because the first 1500 people are already limited by the number of 1-on-1s they have time for during the event. And you can’t just change the fellowship from 30 people to 60 and expect it to be 4x as good; at that point, you’re going to start needing more space and everyone is going to be far from some of the other people, so there’s an asymptotic bound to the value that is less than quadratic.)
(Robi mentioned this to me in person; I thought it was insightful/asked him to comment.) Thank you for the insight Robi! This is an interesting way of thinking about my numbers claim that I had not considered.