The case for range: Why “polymathic” people are so valuable

Updated: Aug 3


A "polymathic person" is also known as someone with intellectual and experiential range. A polymathic person is a valuable "dot connector" that helps draw connections between different disciplines. Our current world seems to value deep specialization. This article provides support for why polymathic people are so important and unique. We also recognize our world does not provide equal access to education resources. We suggest the world will be a better place when we can martial all of humanity's greatest resources…. the mastery potential found in each of our brains.


This article is presented in the following sections:

  1. Background and what makes someone smart?

  2. Skiing down the smart slope

  3. Why range matters

  4. Conclusion

  5. Notes

 

1. Background and what makes someone smart?


Imagine if every person had access to a “smart-defining” app on their smartphone. Upon activating the app, it could provide a report suggesting the key reasons they are “smart.” For sure, the app report would look different for each person.

People tend to define “smart” differently. There is no “one-size-fits-all” description. Some definitions include:

  • Our memory capacity or speed of recall,

  • Our speed of processing or reasoning finite topics,

  • Our ability to find commonality between disparate topics,

  • Our ability to understand and integrate emotion,

  • Our ability to build deep and enduring relationships,

  • It could be something else.

For the purposes of this article, we define smart from both the “inside-out” and the “outside-in.” “Smart” is when an individual reaches a higher-than-average level of mastery concerning some subject. That subject is generally considered successful in reducing entropy for those consumers of the subject.

 

In the notes, we have a reference for the interesting connections between the physics law of entropy and our work. The bottom line is that the work we perform from our “smarts” is directly related to economic value created for others) [i]

 

Thus, our “smart” definition is taken from two perspectives.

  1. Inside-out => The perspective of the mastery-providing individual. Their mastery is generally higher than the average level of mastery of all people in a subject, AND

  2. Outside-in => The perspective of the market for that entropy-reducing subject. The market size (consumer demand) for the products or services supported by the entropy-reducing subject governs the number of people that may perceive one as smart.

For our imaginary smartphone app, both perspectives would be included to rate one’s “smartness” level.


Our definition of smart is relative and based on personal preference. For example, if consumers consider app engineering a means for reducing their entropy and a person has achieved above-average app engineering mastery, then they will be considered smart by those consumers. If someone had developed app engineering mastery in the past, before the common use of the smartphone, they would not have been considered smart by many people. This is because the market did not yet value their mastery.


We may not always consider certain disciplines as having “smart” providers. For example, athletes are not always considered smart. Following this “reducing entropy equivalence to smart” logic, the consumption of sports entertainment may not be considered necessary for reducing entropy. (Even though, professional sports athletes achieve well above-average mastery specific to sports entertainment.)


So, this is a way to define “smart.” But what about different levels of smart? Would most people consider Nobel-winning scientists smarter than those not receiving Nobels? If you are considered smart by the mastery definition but have not received a Nobel, are you less smart? Then, what about polymaths? These are people that achieve deep mastery in multiple disciplines. Is a polymath without a Nobel less smart than a single subject Nobel winner? It does seem our society rewards “narrower and deeper” over “broader and shallower.” [ii]

 

2. Skiing down the smart slope

In this section, we provide a framework describing comparative mastery, for both depth and breadth of knowledge. I think of mastery depth and the number of people that reach this on a normal distribution for a single discipline.

That is, people that achieve deep mastery are in the 4th standard deviation part of the right curve tail, but those that achieve “Nobel-level” mastery are in the 5th standard deviation (“SD”) part of the curve tail. The average person, at the central point of the curve, has general-level knowledge. The curve tail flattens out very quickly, relative to the steeper part of the curve. Thus, to better see the estimated number of people in the tails, we added a log scale callout box. [iii]


So, what does that mean? I am assuming all people exist somewhere on this “smart” curve for at least one discipline. The discipline becomes their means of learning how to think. Their “home” discipline could be biology, literature, mathematics, economics, construction, or whatever. At some point, the skills generated from a particular discipline are sold in the job market. As one learns more and/or becomes more experienced, they move to the right on the smart curve slope. There are about 7.8 billion people on Earth. We are estimating half, or 3.9 billion, have achieved a relative general-level knowledge, mostly through experiencing the environment and some primary education. In effect, learning a single discipline is the means to teach the midpoint group critical thinking. I'm using the "average of smarts" measure to be the midpoint on the planet. I do not know the absolute level of smarts at the average. If we could rank order people by some “mastery score,” I do know at a given time half the people have reached this relative median point of mastery (on the right side of the curve), and the other half have not. (on the left side of the curve). As we discussed in the introduction, “smarts” are difficult to define and are dynamic based on market forces and perceptions. This relative framework enables “wiggle room” to accommodate this reality.


Those reaching deep mastery are rarer (in the 4th SD of the curve). These are people choosing a discipline and reaching a deep level of mastery of that discipline. There are still a decent number of deep mastery-level people at about 500,000. These are people that practice their discipline, through active learning, writing, teaching, or doing. Also, in the current world, there are an increasing number of disciplines available for specialization. The ability of people to specialize seems to be increasing. They may have advanced academic degrees. They may have jobs allowing them to practice their discipline. They may be an autodidact, being self-taught in their discipline. In this article, we do not take a position on how people move to the right on the "smarts" curve. We recognize there are multiple learning methods, with the effectiveness of each method being personal to the individual learner.


Those that reach Nobel-level mastery are very rare (in the 5th SD of the curve). Globally, there are about 5,000 people at Nobel-level mastery. These are people that have PhDs or related education and generally live at the frontier of knowledge for their discipline. Because of this, they tend to be very narrowly focused on their discipline. While not all will win a Nobel, they are still part of a very rare group. They probably rarely teach and dedicate most of their time to discipline research.

 

3. Why range matters


Now, what about polymaths? These are people that reach Nobel-level mastery in multiple disciplines. A few notable polymaths include Benjamin Franklin, Leonardo DaVinci, and John Von Neumann. Polymaths are even rarer. While the world needs specialization, with increased specialization, the world also needs the ability to connect the dots between specialties. Rarely, do individual disciplines alone, create value for improving peoples’ lives. (i.e., reducing entropy) Often an original combination of disciplines is needed to create new and unique capabilities.[iv] Also, a Nobel-level polymath may be “overkill” to connect the dots for many of these new capabilities. A person that has “traveled down the curve” and achieved mastery level knowledge across several disciplines is likely sufficient.


This is where the value of “polymathic” people becomes evident.[v] These are people that are on the downward right-hand slope of the “discipline smarts” mastery curve for multiple disciplines. They connect the dots across multiple disciplines, potentially engaging deeper expertise when needed. They know enough of a range of disciplines to build solutions requiring multiple disciplines. Polymathic people are very important and rare in unique discipline combinations. They also tend to be chameleons, able to adapt their range quickly to pursue multiple solution opportunities. The physicist and mathematician Freeman Dyson said it well. He believes the world needs both specialists and people with range. In his words, we need both focused frogs and visionary birds [vi]:

Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. It is stupid to claim that birds are better than frogs because they see farther, or that frogs are better than birds because they see deeper. We need birds and frogs working together to explore it.

Why is a polymathic person rare? The rareness math is quite simple. Let’s say an individual reaches discipline smarts mastery of 2 standard deviations away from the mean. (by statistical definition, they have achieved mastery beyond 95% of all others for that discipline) Thus, for each discipline, there is a 5% probability of finding that mastery level in the general population. While this is good, on our planet, they are still among a large group of about 350 million people! Instead of continuing deeper in this single discipline, polymathic people switch tracks and build 2 SD mastery in other disciplines. Their curiosity and broad interests naturally take them down another discipline's "rabbit holes." Let’s look at what happens when this same individual reaches 2 SD mastery in 4 other disciplines. Now, they have reached the 2 SD mastery in 5 disciplines. Simple conditional probability math suggests the number of people reaching this level is determined by cross multiplication (.05^5) = .0000003125. As such, the number of people that reach this level of mastery across the 5 disciplines is only about 2,400 based on the earth’s current population. There are fewer people than those in a single discipline with Nobel-level mastery! The point is that people with unique combinations of mastery-level disciplines are rare. The challenge for those building multiple discipline mastery is taking a risk on different disciplines. Since it takes time to build mastery, there is no guarantee the world will value their mastery discipline set. There are certainly ways to improve one’s chances of reaching mastery in disciplines the world values. In the notes section, we provide a reference to a framework for increasing the chances of pursuing high-value careers (disciplines). The framework includes the positive impacts of career earnings when considering job changes and the implied value of continuing education. [vii]

 

4. Conclusion

“The challenge we all face is how to maintain the benefits of breadth, diverse experience, interdisciplinary thinking, and delayed concentration in a world that increasingly incentivizes, even demands, hyperspecialization”

― David Epstein, Range: How Generalists Triumph in a Specialized World


Mr. Epstein is calling for more range - people able to connect the dots between disciplines in a world that seems to increasingly value specialization. This article is aligned with Mr. Epstein’s thesis. We take this thinking a step further by providing a framework suggesting those with “discipline smarts” range across multiple disciplines are as unique as the world’s highly recognized, Nobel-winning specialists. We argue that because of increased specialization the world needs those with range. It is often our entrepreneurs and inventors that may possess this range, that is, those that create new and unique solutions.


We also recognize our world does not provide equal access to education resources. In our model (and as described in note [iii]), the normal distribution is an “upper bound” of people possibly reaching mastery. The world will be a better place when we can martial all of humanity's greatest resources…. the mastery potential found in each of our brains.

 

5. Notes


[i] Hulett, An example of the Stoic's Arbitrage - how our work enables kindness to others, The Curiosity Vine, 2021

Hulett, Fight Entropy: The practical physics of time, The Curiosity Vine, 2021 These articles provide background for how reducing entropy is the purpose of our work.


By the way, if the word “entropy” is causing confusion, you may replace it with the word “value” without losing most of the specificity. As such, in the app engineering example, instead of “decreasing their entropy” one may replace it with “increasing their value.”

[ii] Malone, Laubacher, and Johns, The Big Idea: The Age of Hyperspecialization, Harvard Business Review, 2011


[iii] The shape of the curve and the location on that curve is a stylized deduction. I would very much like to test this hypothesis! My rationale is this: The assumption is of “relative smarts” based on achieving single discipline mastery. Imagine if every person on the earth had a “mastery score.” The entire population could be rank-ordered. The median mastery of the current 7.8 billion people, therefore, is at the 3.9 billionth person on the rank-ordered list. The shape of the curve, using an assumption of normalcy, requires some explanation. Normal distributions require their random errors to follow a normal distribution. That is, single observations must be independent of other observations. In the world of “calm” physics and controlled scientific experiments, observation independence is a reasonable assumption. A great example of the normal distribution with observation independence is the Galton Board, developed by statistician Sir Francis Galton in about 1889. When a blue ball hits a gray peg, it has an equal chance to go left or right, regardless of the ball that preceded it.

However, people and cultures are rarely independent. Imagine each Galton board peg is a "yes/no" input to someone’s mastery learning ability. Inputs may include learners a) from families with 2 parents, b) with parents that already have existing mastery, c) that have access to social capital-enabled education, d) that have family resources to procure education, and/or e) that are from cultures that encourage education. Because of these "dependent" inputs, they are less likely to act independently from the learner that preceded them. In other words, people and cultures tend to create learning momentum or inertia. As such, think of the normal distribution as an upper limit. A lack of learning inertia may create fewer opportunities for certain cultural groups. In a perfect world, all people would have independent access to learning resources. While the normal distribution may not perfectly fit reality, the relative rank ordering is consistent. It is also assumed as more entropy-reducing opportunities reveal themselves, society will be more motivated to create independent learning opportunities. Thus, in the long run, the normal curve should approach reality.


At the 2 SD level, it takes time to build multiple mastery disciplines. This time actually improves the independence challenge because time acts as an independence buffer. In effect, opportunities to utilize mastery occur and change faster than the individual's ability to gain mastery. As such, it is hard for learner momentum or inertia to occur because their unique set of skills is very hard to replicate across individuals (the blue balls) in the short term. This is truly an example of Seneca’s aphorism “Luck is where preparation and opportunity meet.” In this case, preparation must come first to achieve luck.


[iv] For example, Ben Franklin's inventions were very useful in the day. Examples include:

  • Franklin stove

  • Bifocals

  • Armonica

  • Rocking chair

  • Flexible catheter

Franklin's polymathic subject knowledge was necessary. His subject-matter mastery included: Physics, metallurgy, anatomy, medicine, music, chemistry, mathematics, and others.


[v] To define a "Polymath" v. "Polymathic people" - a "Polymath" is one that reaches a deep mastery-level in multiple subjects. John Von Neuman is a great example. He reached Nobel-level mastery in a range of disciplines, including mathematics, physics, economics, and computing. "Polymathic people" are those that have a range of discipline interests, but generally do not reach the deepest level of mastery for those disciplines. As suggested in this article, these are the 95 percenters. Polymathic people are often perceived as being intensely curious about a broad range of interests.

Ken Jennings, the all-time winningest Jeopardy player and famous “polymathic person” said:

"I would say the general rule is if I learn something once and I find it interesting, I think it's more likely to stick. But again, I think that's near universal. You know, somebody who thinks they have an unremarkable memory or a kid who can't learn their times tables, they still know every word of every song on their favorite album and they know every player on the roster of their favorite team. The memory is working just fine when engaged. Like the people you see on Jeopardy tonight. I don't have photographic memories. That's not a real thing. They're just interested in like ten times the things you are. And so more facts stick..."

Levitt, Ken Jennings: “Don’t Neglect the Thing That Makes You Weird” People I (Mostly) Admire, 2021 (bold and italic emphasis added)

[vi] Dyson, Birds and Frogs: Selected Papers of Freeman Dyson, 1990–2014, 2015

As for me, I consider myself a diving bird. That is, I generally like to fly high like a bird, connecting the dots between concepts and helping provide solutions to diverse problems. I do periodically dive into topics. I'm not averse to "being like a frog" and diving into the details. This is often for the purpose of deeper understanding and as an enabler to be a better bird.


[vii] Hulett, They kept asking about what I wanted to do with my life, but what if I don't know? The Curiosity Vine, 2021 This article provides a framework for increasing the chances of pursuing high-value careers (disciplines).

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