In Defense of Hammers Without Nails

Emmy and Carl planned this trip for weeks. After four years of studying Lincoln, Newton, and Homer, they dreamed of living a life without the shackle of a paved path.

And so the day they graduated, they were supposed to drive off and see what the world offered. The world they knew was not good enough, so they pined for the unknown.

As Emmy stepped into Carl’s car, she looked with horror as he began to set up his GPS.

“What are you doing?”, she yelled, “The whole point was to venture into the unknown”

Confused he said, ”How else are we going to get there?”

In a world where research is dependent on case-by-case funding, our intellectual pursuits are increasingly judged on the basis of application.

Do you want to study number theory? You better find some applications for cryptography. Are you working on a new machine-learning theory? You better hope that deep learning can’t do it better.

Over the past months, I’ve been exploring Topological Data Analysis (TDA), which looks to use tools from Algebraic Topology to work with data. More explicitly, it is concerning the shape that data forms in space.

Despite showing some successful results, most of the techniques in the field are either computationally or analytically inferior to deep-learning techniques. This has earned TDA the title of a hammer in search of a nail, in other words, a tool that has no use today, especially in competition with other tools. This type of research is also sometimes referred to as blue-sky research.

Does that mean they have no value? Many would say yes.

But those who deride a field of research as a hammer in search of nails forget that highly efficient and effective tools don’t start as highly efficient and effective. They often don’t even start as tools.

In the eyes of many algebra students, the prototypical hammer in search of nails is the imaginary number. In fact, Rene Descartes, the 17th-century French philosopher, and mathematician, allegedly coined the term imaginary because he saw these numbers as being fictitious and useless.

Surely if we never encounter $\sqrt{-1}$ on a daily basis, it could not possibly have a use other than a theoretical exercise. For hundreds of years, work was done in this field despite it having little or no practical application.

If the work on imaginary numbers was done today, it would most certainly be labeled a hammer without a nail. Nevertheless, any applied physicist will tell you that imaginary numbers are at the heart of too many practical applications to count.

Much of this labeling is due to Status Quo Bias. “Deep learning works the best now, so it couldn’t possibly be worthwhile to exert effort in a different direction”. In the face of GPT4 and recommendation algorithms that know us better than we know ourselves, you can’t blame someone for thinking this way.

Compound the Status Quo bias with increasing competitiveness for research grants, and you have an economic landscape that leaves little incentive for hammers without nails. Thus, we steer the direction of research towards short-term applications, locking practitioners onto their current (and likely suboptimal) path.

Academic fields need time and resources to develop. The best policy is to value additions to the collection of human knowledge because knowledge is inherently valuable. History shows us that pursuing knowledge indiscriminately will always lead to the best outcomes.

Research has no upper bound on usefulness

Adam Mastroianni recently wrote about Strong-link and Weak-link problems. He gives the following definition:

Weak-link problems are problems where the overall quality depends on how good the worst stuff is. You fix weak-link problems by making the weakest links stronger, or by eliminating them entirely…Some problems are strong-link problems: overall quality depends on how good the best stuff is, and the bad stuff barely matters

In his piece, he argues that science (And I would extend that to research in general) is a strong-link problem. We can extend this idea to thinking about bounds to the consequences of hammers in search of nails.

The negative consequences of hammers without nails are bounded. If the produced research is never used again, we’ve wasted a finite amount of time and resources of the researcher.

The positive consequences of hammers without nails are unbounded. Unless the produced research is verifiably false, there is no way of telling how applicable it may be in the future. There are too many examples of research whose future application was not anticipated:

• Einstein’s Relativity theory was later used in GPS technology
• Graphene was viewed as unfeasible to be used at scale
• Mendel’s work on Genetics was overlooked for decades
• Prime Number Theory is essential to cryptography
• Computer Science predates computers themselves.

From a utility maximization standpoint, it makes sense to bet on hammers in search of nails. The massive scientific strides are only possible by taking this gamble.

We need to get comfortable with the idea that the seeds of research might take centuries to grow fruit. Someone needs to plant these seeds. The work may not come with fat salaries and Nobel prizes, but it is nevertheless crucial.

Following truth into the unknown is the only way to find our future selves better than we are today.