Knowledge compounds exponentially: an explanation for the matthew effect

By Duncan Anderson. To see all blogs click here.

Reading time: 3 mins

One sentence summary: Knowledge doesn’t just compound, it compounds exponentially, what you can learn is a function of what you know. The more you know the more valuable each incremental unit of learning is. 

The Matthew Effect is well documented in Education

• While this image is referring to reading, the same effect is seen in maths, science, sport, emotional intelligence, art, etc! 

You’re probably also familiar with the magic of compound interest

• Bill didn’t start saving until 10 years after the others so he can’t achieve the same results. Sorry, Bill. 

A tangible example of knowledge compounding

• Let’s say Person A likes footy and Person B doesn’t like footy, meaning the existing knowledge base of Person A is much bigger than Person B. 

• Both Person A and Person B read the same article on footy. 

• The outcome is that Person A increases their knowledge base by more than Person B from the same unit of knowledge acquisition (in this case reading the same article). 

• Knowledge base = number of facts * value of each fact

• So the person with the higher knowledge base will compound away if both Person A and Person B do the same work from this point going forward. Ie the gap between Person A and Person B will only ever increase even if Person A and Person B do the exact same quantity and quality of upgrading going forward. 

• A rearticulation: if I read a book today I get much more value from it than reading the same book ten years ago as I know much more today so I’m able to see more things in the book and join each thing onto more of my existing knowledge. 

• Jingle: what you can learn is a function of what you know. The more you know the more you can learn. What you can do is a function of what you have done. The more you have done, the more you can do. 

One model for knowledge: the value of each piece of knowledge is the number of other pieces of knowledge that it can be attached to. 

• Most knowledge isn’t discrete, the value of each piece of knowledge is the number of relationships it has with other pieces of knowledge. 

• Some pieces of knowledge are very limited, eg today is Sunday. The interesting things to learn can often be connected onto an almost limitless number of other ideas… oh and humanity is coming up with new stuff every day! 

• As an example I think I’ve used the idea of fractions in 1000+ ways. I think I’ve used the idea of ‘growth mindset vs fixed mindset’ in 100+ ways. I think I’ve had 5 generations of thought on what relaxing is! 

• Edrolo note: 

  • The compounding of knowledge talks to the nature of knowledge being more infinite than finite. 

  • Normally, the more knowledge you have the better you are at making connections. Or on this visual, the better you are a developing ‘wisdom’ through connections.

Improving knowledge = Quantity * Quality. Some thoughts on quality. 

• Modalities of knowledge levelling up: reading, thinking, talking, building & writing. 

  • Quantity: “Read 500 pages every day. That’s how knowledge works. It builds up like compound interest.” – Warren Buffet

• Quality: I think one should have a good balance of each of these modalities. In hindsight I was massively under investing into the writing modality until ~5 years ago. I think one should write for 10% of one’s work week. 

• Some blogs on this. 

  • Diverse Reading vs Undiverse Reading AKA Building Knowledge vs Digesting Facts

  • Some writing about writing: A blog on this, another blog on this, another blog blogging… and another.

A rearticulation: increased knowledge base ≈ increased reading comprehension ability

• For now I’ll define: Reading comprehension = how much you can ‘ascertain’ from reading a passage

• The more you can ascertain the better you are at reading comprehension. Or in the terminology of above, how many facts you can find AND how many outside facts you can join each of the facts found in the article onto. 

• This is also another articulation of how much ‘information’ you can find from this blog. Effectively what you can see in the world is a function of what you have already seen in the world. The more time you have spent trying to see, the more you can see. I believe the world can become only ever more interesting, only ever more detailed, only ever more beautiful… if you put in the effort to upgrade your knowledge, to upgrade yourself! 

• As an example: if you know something about politics, economics, sociology, mental health, finance, management, startups, etc etc then the chance you’ll be able to see more when you read a book is high vs if you don’t know anything about these fields. 

If you only take away one thing

• The more I know, the less I know. 

• Compounding knowledge helps you big time! The sooner you get going the better.