What Hamming's "The Art of Science and Engineering" tells us about the liberal arts and humanities

Today at 4 AM, I woke up to fly from JFK to LAX and move into Pomona College, a liberal arts school where I plan to major in Media Studies and Physics. The majors reflect my dual interests in technological innovation and social change. The book I began to read on the flight was in the gravity well of the former: mathematician Richard Hamming's The Art of Doing Science and Engineering, which a trusted friend conducting cutting-edge biotech research had recommended I put "at the top of my reading list."

The book didn't disappoint, spurring a series of clarifying insights about technological innovation. In the following day of orientation, of deans espousing the glories of liberal arts education and myself relishing the non-technical pursuits that lay head, I was surprised to realize that Hamming's insights applied just as sharply to humanities work as scientific. I found myself building a framework not only for my aspirational career in research and engineering, but also for social science scholarship and journalism, and re-surfacing core unanswered questions that lay at the root of the latter.

If you'll forgive me for the roughness of my piece -- it's late at night and I'm hoping to simply get these ideas down before I lose my passion for them -- here are my takeaways from the first few chapters of The Art of Doing Science and Engineering, and my thoughts on their application to the liberal arts and humanities.

Who's Hamming? What's this book about?

Hamming was a pioneering mathematician and computer scientist who worked on the Manhattan Project in 1945 and Bell Labs until 1976. The error-correcting Hamming code was what I knew his name from. The Art of Doing Science and Engineering contains a course Hamming taught at the Naval Graduate School following his retirement, a course with ambitious objectives:

"The purpose of this course is to prepare you for your technical future. There really isn't this course any technical content...I am concerned about style. I have studied great scientists, ever since I was at Los Alamos during the war. What is different between those who do and those who do not do significant things? Mainly, it's a manner of style."

What follows in the first chapter, titled "Orientation", is a series of eloquent mental models and assertions about life, learning, and innovation.

Study successes, not failures

Learn to succeed by studying successes, not failures. "I regard the study of successes as being basically more important than the study of failures. As I will several times say, there are so many ways of being wrong and so few of being right, studying successes is more efficient, and furthermore when your turn comes you will know how to succeed rather than how to fail!"

"Back of the envelope" calculations

Do "back of the envelope" calculations often to check any stats that are thrown your way. For example, take the claims "knowledge doubles every 17 years" and "90% of scientists who ever lived are now alive." Are they compatible? Make your assumptions -- the number of scientists is directly proportional to the amount of knowledge; a scientist lives 55 years after their childhood (i.e. becoming a 'scientist') -- then write some equations and find that, indeed, 89.4% of scientists are predicted to be alive at any given time if knowledge doubles every 17 years and other assumptions hold true. The point of doing these calculations is both to reveal hidden assumptions in claims, and strengthen your ability to model situations or systems.

Here, the modeling is explicitly quantitative. As an aspiring student of and impact-maker within the humanities, though, I naturally wondered about carrying over Hamming's mindset to social sciences and art.

The connections are easy to find: as a critical theorist, you're constantly training your ability to notice and deconstruct the invisible forces around you. As a journalist, you're training your ability to align storytelling with the service of democracy, whatever that means to you. As an artist, you're training your ability to capture and express hidden meaning in the experiences and ideas around you.

Perhaps none of these examples reach the level of rigor of scientific, mathematical modeling: critical theory, journalist storytelling, and art all seem much more subjective and less useful than a set of equations. I don't believe that this is necessarily the case: mathematical modeling has its fair share of subjectivies, and the theory of social science and practice alike can be developed to a high degree of consistency that constructs useful objectivity.

Regardless, the mindset is the same: practice seeking truth rigorously, without reliance on others' authority. This is how you will be able to keep up with and drive progress in any field.

The difference between science and engineering

What's the difference between science and engineering? "In science if you know what you are doing you should not be doing it. In engineering if you do not know what you are doing you should not be doing it," Hamming writes. It's a brilliantly clear explanation of not just science and engineering, but also implicitly any dichotomy of practice and innovation.

I'm reminded of my own mental model of "velocity" vs. "acceleration"-based execution that I came up with for StartupTree. Velocity-based execution is about upholding the status quo, taking initiative to solve problems and plug gaps creatively, but not ultimately accomplishing anything new. Acceleration-based execution is about upending the status quo, solving problems in experimental new ways altogether, or choosing new problems to solve, until the velocity is caught up and the disruptive becomes the everyday to uphold. Both are necessary and intertwining.

The doubling of knowledge

Making the above example more than an example, Hamming expands on the doubling of knowledge every 17 years: "This doubling is not just in theorems of mathematics and technical results, but in musical recordings of Beethoven’s Ninth, of where to go skiing, of TV programs to watch or not to watch."

Furthermore, the half-life of knowledge learned in school is 15 years, Hamming states. In 15 years, half of what you learned will be useless.

How to counter this rapid progression of knowledge? "You must concentrate on the fundamentals," Hamming asserts. Fundamentals are those ideas that "have lasted a long time" or from which the rest of the field can be derived. Furthermore, learn how to pick up new domains of knowledge effectively.

These ideas are oft-evoked elsewhere, from TKS' "first principles thinking" to the liberal arts doctrinal objective of "teaching students to think critically so they can solve problems that don't yet exist."

Emphasizing this ethos, Hamming notes in a later section: "Both the science and the engineering you will need for your future will more and more often be created after you left school. Sorry! But you will simply have to actively master on your own the many new emerging fields as they arise, without having the luxury of being passively taught." The passage reminds me of Jay's recent decision to leave his ML startup to work in climate, rejecting career growth and instead choosing to directly tackle the challenges that matter to him, never having expected a conventional career trajectory to sufficiently support his learning.

To be a leader, have a vision / pick a direction and get going

Another idea very familiar to me; connecting it to the liberal arts, this was my answer to "what's the best advice you've ever received?" on my Pomona application: "If you don’t know what path to choose, choose one and start heading down it. Finding meaning is a matter of experience and iteration; you’ll learn much more by moving forwards than by ruminating at the junction."

Hamming puts it thusly:

"It is well known the drunken sailor who staggers to the left or right with n independent random steps will, on the average, end up about sqrt(n) steps from the origin. But if there is a pretty girl in one direction, then his steps will tend to go in that direction and he will go a distance proportional to n. In a lifetime of many, many independent choices, small and large, a career with a vision will get you a distance proportional to n, while no vision will get you only the distance sqrt(n). In a sense, the main difference between those who go far and those who do not is some people have a vision and the others do not and therefore can only react to the current events as they happen."

Even in the scope of this very course, Hamming emphasizes the outsized importance of pursuing a vision: "One of the main tasks of this course is to start you on the path of creating in some detail your vision of your future. If I fail in this I fail in the whole course." Furthermore, in agreement with my Pomona application response, Hamming adds that it doesn't matter if the vision you pursue is wrong: "from observation I have seen the accuracy of the vision matters less than you might suppose, getting anywhere is better than drifting, there are potentially many paths to greatness for you, and just which path you go on, so long as it takes you to greatness, is none of my business."

Arriving at a vision for the future: science, engineering, and ethics

To arrive at a vision for the future, one must answer three questions, Hamming writes:

"What is possible?" "What is likely to happen?" "What is desirable to have happen?"

These three questions are answered by science, engineering, and ethics, respectively.

From our earlier definition, it's easy to see how science and engineering fall onto their respective questions. The separation of the third category, though, is interesting to me.

In the context of what's traditionally thought of as science and engineering, this separation makes total sense. But what about in the realm of social science, or art?

The idea of "science" as innovation and "engineering" as status-quo execution carries over nicely to social science, just like the eralier back-of-the-napkin calculations mindset. Consider an extension of the earlier example where critical theory constitutes "science", where hypotheses are posed about the workings of society firmly in the territory of high-level thought, the realm of the "unknown"; over time, the practical "engineering" of journalism or education might bring these theories down to the level of having an impact on society, say by shaping election results or job recruiting practices, but at this point in time no development in the theory itself is being made. All that's being done is "known".

The danger of social science and engineering is that, in their presentation, the third category of "ethics, morals, or what ever other word you wish to apply to value judgments" is often perceived to be lumped in. Critical race theory in and of itself doesn't advocate for any course of action. If you seek to build a white supremacist society, the theory functions as an instruction manual, just as surely as it does a powerful diagnostic tool for those seeking to tear white supremacy down. Marx and even Lenin's revolutionary writings, without the context of the reader agreeing with their revolutionary values, similarly outlines theory for revolution, but does not spark revolution in its isolated form.

Thus, this third category -- the contextual values surrounding social science and engineering -- require careful separation and examination in order for social science to be taken rigorously and society to progress constructively. The trouble is that the analysis of these contextual values is the very domain of social science. It's a catch-22 in which only generally unstably self-consistent stables can be built, rather than dynamically stable axiomatic ones as in math and physical science.

What's the solution to this recursion? Are there fundamentals lying at the root of it all to search for? There certainly are within specific disciplines of social science. To understand these are why I decided to go to Pomona and major in media studies, over a pure engineering school. At the end of the day, though, the best solution Pomona seems to have is to continue critically thinking forever, to not trust axioms but rather continuously iterate.

Does this iteration really lead to sustainable progress? What are the fundamentals that lay at the root of this iteration?

Once again, I've arrived at the line of inquiry that constitutes my present personal mission statement. "Why do people believe the things that they do?"