Knowledge: Burden or Boost?

Economist claim that society is burdened by too much knowledge. Does this make sense, and is knowledge actually a boost, not a burden?

Some have argued that society is subject to a burden of knowledge. The paper that originated this idea was published in 2009 by economist and professor at the Kellogg School of Management, Benjamin F. Jones. The burden of knowledge describes the idea that the time that it takes to reach the "frontier" is getting longer, i.e., one needs to acquire more knowledge to innovate.

There are several problems with this paper and idea, like the assumption that ideas are zero-sum. Below I explain why the burden of knowledge concept is wrong and criticize it by appealing to the idea that knowledge grows via creativity, conjecture, and criticism.

Most importantly, the idea that more knowledge just accumulates and thus requires more time to learn is wrong.

What’s wrong with the burden idea

Knowledge grows unpredictably

The paper assumes a fixed amount of ideas:

Ideas come to an innovator at rate R(d,t) [t stands for time]. This arrival rate [R] depends in part on an innovator's educational decision, d, which is fixed over an innovator's lifetime, and in part on the overall state of the economy, which evolves with time.

The authors also model knowledge geometrically as a cylinder whose size is a function of the knowledge depth and breath. They illustrate this with the required knowledge to invent the first airplane vs. creating a modern-day airplane.

Ideas do not simply come to us. As the philosopher Karl Popper says, they are conjectured using creativity¹. We call something a prophecy if it purports to know what is not yet knowable²:

The future of civilization is unknowable, because the knowledge that is going to affect it has yet to be created. [...]

[...] People in 1900 did not consider the internet or nuclear power unlikely: they did not conceive of them at all.

No good explanation can predict the outcome, or the probability of an outcome, of a phenomenon whose course is going to be significantly affected by the creation of new knowledge.

Thus knowledge does not grow linearly or as a function of time (or geometrically). Humanity goes through sudden Cambrian explosions of technological progress such as we saw in ancient Athens, medieval Florence, and modern Silicon Valley.

Children can innovate

Secondly, in the paper's model, "Once educated, innovators begin to receive innovative ideas".

I.e., the paper’s author assumes knowledge creation starts with the graduation of an innovator. This is wrong. Innovation starts much earlier:

• Elon Musk famously sold his first computer game when he was 12.

• Shubham Banerjee created a low-cost Braille printer when he was 13.

• At the age of 14, Canadian inventor Taylor Wilson built a nuclear fusion reactor in his parent's garage.

• The Indian mathematician Srinivasa Ramanujan independently developed and investigated the Bernoulli numbers at the age of 17.

• The Collison brothers sold their first software company for $5 million at ages 17 and 19.

One reason these cases are rare is our broken education system. Governments force-feed students a fixed curriculum of “important" knowledge.

Most of the listed children above were autodidacts, avoiding the self-limiting system and embracing their unbounded curiosity.

Wrong zero-sumness: fishing-out effect & low-hanging fruits

Wrong zero-sum model

The assumed "fishing out effect" and the related “low-hanging fruits phenomenon” describe the view of ideas as a zero-sum quantity that can be used up. A belief in the zero-sumness of our society's wealth is one of the biggest misbelieves of humanity. For tens of thousands of years, before the invention of credit, people did not trust in future wealth creation. The pie is not fixed, nor is the economy "distributing" it. It grows with every new person, idea, invention, company, and market. David Deutsch accurately describes the current state of science and its abundance of problems:

It happens that our current scientific knowledge includes a historically unusual number of deep, fundamental problems. Never before in the history of human thought has it been so obvious that our knowledge is tiny and our ignorance vast³.

How our knowledge grows

Knowledge can be augmented

The paper wrongly states that knowledge can only be used in people's heads.

New problems require new knowledge to solve, but using new knowledge requires understanding (at least some) of the earlier, more basic knowledge. Over time, the total amount of knowledge needed to solve problems keeps rising. Since knowledge can only be used when it’s inside someone’s head, we end up needing more researchers. And that’s precisely the dimension that Bloom et al. (2020) use to measure the declining productivity of research - it does take more researchers to get the same innovation⁴.

This claim is based on a false, widespread belief; The idea that knowledge is a psychological phenomenon or that knowledge is a true, justified belief. Knowledge exists as an abstract reality external to minds. it can be stored in many substrates. For example, the knowledge of how to construct a spaceship is embodied in the spaceship itself. Our brains can store knowledge, but so can computers we interact with. The field of Cognition Augmentation Software (a sub-field of Human-Computer Interaction) studies how we can augment our cognition and our memory using computers. Everyone with an internet connection, for example, the next 16-year-old Einstein, has access to this knowledge, so more researchers are not the only solution to bridge the gap between knowledge and innovation. 

Old knowledge is disregarded

False and old knowledge is frequently disregarded and thrown out whole cloth as better explanations arise. It is refuted. 

Our scientific history is littered with examples such as the earth-centered universe, the study of phrenology (the pseudoscience that linked personality traits with different brain "organs"), the static universe, the 'fish stage' of human development, and many more. The fact that you likely haven't heard about one of these makes the point.

This process in our collective cognitive processes of organizing humanity's knowledge is fascinatingly analogous to the cognitive processes in our individual human brains, namely that of forgetting. We each only store the most (subjectively) useful knowledge and the latest versions of our theories. The knowledge that unnecessarily burdens us is abandoned.

Fewer, deeper, more general theories

The idea that more knowledge just accumulates and requires more time to learn is wrong. Instead, we are replacing old knowledge with new, fewer, deeper, and more general theories as David Deutsch describes in The Fabric of Reality.

Depth: Deep theories cover unfamiliar situations as well as familiar ones. This can lead to us understanding something without knowing we understand it.

Breath: More general theories explain more about a wider range of situations than several distinct theories previously.

More theories ≠ more learning required. A theory can be a

1. Superseding theory: Nicolaus Copernicus superseded the complex Ptolemaic system with Earth at the center.

2. Simplification: Arabic (decimal) notation simplified Roman numerals.

3. Unification: Electricity and magnetism becomes electromagnetism.

As part of this process, we also improve our techniques, language, and concepts to understand other subjects.

This process gives subjects properties such as beauty, inner logic, and connections with subjects which make these concepts and ideas easier to learn.

Knowledge is being compressed

Another variation of this is that a readily understood phenomenon or idea is more compressible. This theory is rooted in information theory. The German AI scientist Jurgen Schmidthuber even hypothesizes that the desire to compress is the origin of curiosity and fun (a topic I'll write about more soon). In fact, for Schmidhuber, the idea that we go through the world striving to better compress our representation of the world offers a “formal theory of creativity and fun.” He explains: “You just need to have a computational resource—and before learning a pattern, you need so many computational resources, and afterward, you need less. And the difference, that’s where you’re saving. And your lazy brain likes to save things. And, that’s the fun!”

For example, Kepler compressed many astronomical theories into a model consisting of a few ellipses.
A related concept is that of Abstractions. Rather than only helping us with the storage of knowledge, they also help us to understand phenomena and process knowledge. One such abstraction is causation. We cannot perceive causation, only the succession of events. It is an abstraction that allows us to understand phenomena in our environment. It’s still unclear to me how exactly this concept fits into the before-explained compression theory.

Here's what might be happening instead

The paper postulates that longer education leads to more knowledge burden and specialization. What if the causality goes the other way? I.e., greater specialization leads to longer education. What if the culprit is broken research funding allocation? Precisely defined proposals about specialized specific problems can get funding easily, but interdisciplinary and risky research dies out. Fortunately, institutions such as the Arc Institute or the New Science program are trying to reverse this trend.

It's also likely that we are unnecessarily burdening students with useless knowledge. The pseudonymous blogger by the name of Roger's Bacon recently wrote in response to Dwarkesh Patel’s Annus Mirabilis article:

[W]hy has no one had a miracle year in the last 100 years? Because now people have to spend their 20s learning about the discoveries that others made during their miracle years ….

First, we shouldn’t force students to learn anything. Basing our education systems on the behavioristic bucket theory of the mind and force-feeding them a fixed curriculum is wrong. Second, this holds especially true for old refuted theories if we already have better explanations. This is not only immoral but also wastes time. There might indeed be a decline in quality and lack of innovation in our education system, i.e., the transfer of human capital.

In The Making of the Atomic Bomb, Leo Szilard describes the experience of Hungarian high schools in the 1880s, which trained many of history’s best scientists like Jon von Neuman, Edward Teller, and Eugene Wiegner:

to begin mathematics they looked up figures for Hungary’s wheat production and made tables and drew graphs. At no time did we memorize rules from a book. Instead we sought to develop them ourselves. What better basic training for a scientist?

But most importantly, we can augment our brains. The knowledge they can work with is not limited to the primitive 2500 terabytes our brains can carry. The internet holds about 135,000,000,000 terabytes and is more than doubling every five years. New knowledge about cognition augmentation technologies will make augmenting more of our cognitive processes increasingly easier. A self-perpetuating cycle.

David Krakauer, the president of the Santa Fe Institute, comes to a similar conclusion. 

“You suggest that the problem is invention. But I see no evidence that people are less ingenious. I see the problem as moving their genius into the world. The problem is the second stage of Schumpeterian innovation.” The fault is not in our minds but in our markets.

I think this is not completely accurate. The ideas in our minds form our markets. When genius is not being unleashed, it's due to cultural ideas that suppress creativity, and/or due to a lack of technology that frees people up to think for a living.

Open questions

It’s still unclear to me to what extent the requisite knowledge to conjecture an invention needs to be loaded into an innovator's working memory and how much can be:

1. Distributed among multiple innovators that come up with a solution together, and

2. Stored in external memory aids.

Distributed cognition (or Social Computing) assumes that cognitive processes can be separated in space and time but act together to produce one output, I.e., that we can augment each other's cognitive processes or offload certain functions to computers. 

As an example, two or more researchers (R) trying to come up with a good explanation (E) for a phenomenon might point out different constraints and variations to their proposed explanations, thereby combining their cognitive processes (CP).

1. Popper, Karl. 2002. Conjectures and Refutations

2. The Beginning of Infinity, David Deutsch, p. 197

3. The Beginning of Infinity, David Deutsch, p. 448

4. https://www.newthingsunderthesun.com/pub/zsc23qxz/release/11 (or paragraph link: https://www.newthingsunderthesun.com/pub/zsc23qxz#why-are-ideas-getting-harder-to-find)