Price's law: the productive square root

Derek Price was a scientist, active between the 1940s and 1970s, known for his work in "scientometrics", which is, broadly speaking, the science of measuring and analysing scientific literature. 

He proposed a theory for the exponential growth of science - which today is mirrored in a few other theories, perhaps the best known of which is Moore's Law on the exponential growth of computing power.

Fun fact, this passion was formed when Price was on a 3-year stint in Singapore at the Raffles College (today, the National University of Singapore) between 1948-1951. He was reading in the Raffles College library and noticed that, when placed in chronological order, the volumes of a scientific journal got thicker and thicker!

Derek Price also formulated Price's Law, which is the proposition that a small group of people in a given group are responsible for most of the group's results e.g. that half of scientific literature is produced by the square root of the number of authors. 

This means that in a group of 4, everyone contributes about equally. But as the group enlarges, a smaller and smaller proportion of the group becomes responsible for the majority of the work. So in a group of 25, the square root i.e. 5, is responsible for half the work, while 20 do the rest. In a group of 10,000, only 100 are responsible for half the work, while 9,900 do the rest! 

In short, the larger the group, the more the work is concentrated in a small group of people, and the larger the group of people who do the remainder.

As group size grows, the increase in productivity is linear, but the increase in unproductivity is exponential (note how this differs from what is proposed in the Pareto Principle, which suggests that 20% of overall effort produces 80% of the result - which is a linear relationship).  

Putting aside the specific accuracy of the mathematics, many people have noticed that this principle seems to apply in many other fields as well:

- The majority of important classical music/novels/art seems to be produced by just a handful of composers/authors/artists. 

- The majority of scoring in a football or basketball team is done by a small number of players in the team. 

- The majority of wealth is concentrated in a small number of people. 

- An overwhelming percentage of total US market capitalisation is in the top S&P500 companies.

Just to be clear - I don't think this necessarily means that people outside Price's square root of productive people are unimportant. 

Rather, it implies that as a group enlarges, we have to think and organise ourselves much more deliberately (e.g. small project and organisational team sizes, being hyper-sensitive to mission creep and organisational sprawl), so as to mitigate the impact of this natural social phenomenon, and to allow each individual to continue to contribute most impactfully. 

This is probably something many tech companies are having to work through now, having grown exponentially and carelessly through a protracted era of cheap funding, and an obsession with achieving scale as an end in itself.

All this feels a bit corporate-speak-ish. But it applies everywhere else in life. Work certainly is important. But what about our contribution to our communities? What about our contribution to our churches? 

Price's law reminds us that human tendency is to gravitate toward unproductivity, and exponentially so as the size of the group increases. What are we doing to mitigate that, and continue to be impactful? How do we make a difference?

Who do I want to be? The guy on the field, or the guy on the side, watching the guy on the field? Theodore Roosevelt famously said:

It is not the critic who counts.

Not the man who points out how the strong man stumbles, or where the doers of deeds could have done them better.

The credit belongs to the man who is actually in the arena, whose face is marred by dust and sweat and blood; who strives valiantly; who errs, who comes short again and again, because there is no effort without error and shortcoming; 

But who does actually strive to do the deeds; who knows great enthusiasms, the great devotions; who spends himself in a worthy cause;

Who at the best knows in the end the triumph of high achievement, and who at the worst, if he fails, at least fails while daring greatly, so that his place shall never be with those cold and timid souls who neither know victory nor defeat.

My pastor preached this really well this weekend too. If you want to see an angel rescue you - you have to go into the furnace (Daniel 3). If you want to see lions' mouths shut - you have to spend the night in the den (Daniel 6). If you want to see praise bring down walls - you have to assault a stronghold (Joshua 6). 

Do not pray for easy lives. Pray to be stronger men.

Do not pray for tasks equal to your powers. Pray for powers equal to your tasks.

I recently met an old acquaintance for lunch, and she was telling me how she had recently encountered God, after going through various personal trials. 

She told me that she actually first met me many years ago, at a Christmas party. I said, I don't remember that at all! 

So she explained that it was at a mutual friend's house, and all she remembered about me was this enthusiastic guy who had turned up and started telling everybody about the Meaning of Christmas, and she was thinking - who the heck is this dude :D

I remember thinking to myself, wow, if only I was like that all the time, so that all anyone who ever met me would remember - there's this dude who seems to be overflowing with enthusiasm for Jesus - there must be something there!

My daughter recently told me she too had met an old school junior for lunch, and they were sharing the various travails of the life of a young lady these days. My wife asked my daughter - oh, you should ask her to go to church with you. 

And my daughter said, yeah, funny thing, when we were talking, my friend said she told her mother she was meeting me, and her mother said, oh that one, the girl who’s always asking you to go to church :D

That's who I want to be too. It's 2023! In this new year, I want to intentionally work at being a fellow that people remember, not for me, but for the God who lives in me, who leads me, and enables me to be that "city on a hill that cannot be hidden" (Matthew 5:14). 

A fellow who, in my own small way, fights at the front, makes lots of mistakes, but also makes a difference. A fellow who works in small, effective groups, and not necessarily big, splashy things. Helping individual lives, and not necessarily world-changing projects. So that I can always be part of that productive square root!

For we are God's handiwork, created in Christ Jesus to do good works, which God prepared in advance for us to do. Ephesians 2:10