Science is a form of art in which one uses mathematics to paint reality.

The Artistic Expression of Science

Science is often perceived as a purely rational and logical endeavor. We say that a subject is more of an art than a science to express that practitioners are guided by intuition rather than knowledge or logic. Science, it seems, is the opposite of art. And scientists are perceived as hyper-rational truth seekers driven by data and logic above all else.

There is probably no sentiment that I disagree with more strongly than the one expressed above. In my view, science is art. Being a scientist is to dedicate yourself to a life of creativity above all else. Well, to a life of practical creativity let's say.

Science as Artistic Expression

I view science as a form of art in which one uses mathematics to paint reality. This perspective highlights the deep connection between the creative process inherent in both scientific and artistic endeavors. Just as an artist uses brushes and colors to capture the essence of their subject, a scientist uses mathematical models and equations to describe the complexities of the natural world.

At its core, doing science involves a profound sense of curiosity and imagination. Scientists, like artists, are driven by a desire to explore and understand the unknown. This exploration is guided by intuition and creativity more than logic, leading to the formulation of hypotheses and theories that seek to reveal the underlying beauty of the universe.

Mathematics serves as the palette and brushes for the scientist. It provides the tools to create detailed and precise representations of reality. Through equations and models, scientists can depict the intricate patterns and structures that govern natural phenomena. Mathematics allows for the expression of ideas that are not only accurate but also elegant and beautiful.

The process of scientific discovery is akin to the artistic process. It begins with an inspiration, a question that sparks the imagination. This is followed by the creative phase, where scientists brainstorm and develop theoretical frameworks. Experimentation and empirical testing add layers of depth and detail, much like an artist adding strokes to a canvas. Throughout this journey, scientists constantly refine their models, striving for simplicity and elegance, just as artists seek to capture the essence of their subject with minimal yet expressive strokes.

Science, like art, is inherently subjective. Different scientists may approach the same problem with varying perspectives, leading to diverse theories and models. These different interpretations are influenced by personal intuition and aesthetic sense, much as artists bring their unique vision to their work.

Ultimately, the goal of science is to uncover the beauty and order in the natural world. The theories and models that resonate most deeply with scientists are those that not only make accurate predictions but also possess an intrinsic elegance. This dual pursuit of truth and beauty is what makes science a form of art.

Developing Intuition and Aesthetics

Science is the art of discovery, and its engine is intuition. Intuition guides researchers toward fruitful lines of inquiry, away from bad ones, and helps them recognize patterns and connections that may not be immediately apparent. How does one develop this intuition?

First, by thinking. I don't mean thinking as in logic, I mean thinking as in imagination, by training yourself to visualize hypothetical experiments. Imagine yourself doing them, what data will you measure, what will the graphs look like, how will they change if you adjust your setup? Then, of course, do the experiments! You have to refine your senses until you can visualize what really does happen more often than not.

Second, cultivate an aesthetic sense by exploring diverse theories and models, even those outside your immediate area of interest. Understanding different approaches can help scientists develop a sense of what they find elegant and compelling. But, don't worry too much about what other people like. Decide for yourself.

Third, build your creativity. Get outside of the box! Figure out how you could do the thing differently. Explore fields outside your own. Try engaging in other artistic activities such as music, drawing, or writing. Sit inside your imagination, review your experiments, and re-read your notes until you feel them in addition to knowing them.

Fourth, keep creating ever simpler explanations, analogies, and metaphors for complex concepts. Developing the ability to explain your work to anyone isn't an afterthought; it is a key part of doing the work itself. By striving to simplify and communicate our understanding, we clarify our thoughts and uncover the core principles underlying complex phenomena. This process of simplification forces us to question our assumptions, refine our ideas, and achieve a more profound and intuitive grasp of the subject matter. In essence, the act of explaining science in simple terms is like the sculptor chipping away at the marble to reveal its final form.

Examples of Artistic Scientists

Some really famous scientists have followed this philosophy to great success.

Richard Feynman exemplified the fusion of science and artistic expression. Known for his intuition and playful approach to problem-solving, Feynman often emphasized the beauty and joy of discovery. His famous thought experiments and unconventional methods reflected his belief in the importance of intuition. Feynman’s extracurricular activities, such as playing the bongo drums, showcased his creative spirit and highlighted the interconnectedness of artistic and scientific pursuits. And, of course, “the great explainer” was famous for breaking down the most complex topics in theoretical physics so that anyone could understand and appreciate them.

Not to be outdone, Albert Einstein also valued intuition and the aesthetic beauty of scientific theories. He often spoke about the simplicity and elegance of fundamental laws of nature. Einstein’s use of thought experiments, like imagining riding alongside a beam of light, demonstrated his reliance on intuition and creativity. His love for music, particularly playing the violin, paralleled his scientific endeavors, showing that creativity in one domain can enhance creativity in another.

Everybody’s Different

This note is about my approach to science. This is what I like. As stated above, I'm not alone. But not all scientists like it agree with this philosophy.

For example, Isaac Newton's approach to science was highly analytical and based on systematic experimentation and observation. He valued meticulous calculations and a focus on finding definitive answers through precise mathematical laws.

Likewise, Francis Bacon developed the empirical method and inductive reasoning, emphasizing the collection of data and observations to build knowledge. Bacon's approach was grounded in the systematic accumulation of facts and data, contrasting with the more theory-driven and intuitive methods advocated by Feynman and Einstein.

Perhaps it's field dependent. For example, many mathematicians are trained in rigorous applications of logic may view the world differently, as with engineers tasked with building the most reliable or efficient implementation of a technology.

So, if my approach doesn't resonate with you, who cares. You be you, let me be me. Explore for yourself and find your own way of thinking. (Though, we might struggle to collaborate effectively… more on that later.)

My Philosophy

My philosophy of science emphasizes the intersection of intuition, beauty, and empirical validation. Scientists should develop their intuition and aesthetic sense, finding theories that resonate personally while also making useful predictions.

In both art and science, intuition is a powerful tool. Trusting your inner voice and following what feels right can lead to breakthroughs that logical thinking alone might not achieve. Whether you're making music or discovering scientific principles, it's about finding what resonates deeply within you.

For me, simplicity is the ultimate sophistication. In science, as in art, the most profound ideas are often the simplest ones. They have a beauty and clarity that cuts through the noise. Strive for that simplicity in your work, and you'll find something truly remarkable.

Don't limit yourself to one way of thinking. Explore different fields, collaborate with people outside your discipline, and bring those diverse influences into your work. Creativity flourishes when boundaries dissolve, and new connections are made.

Art and science are not so different. Both require a deep mastery of your craft, and both are about expressing something profound about the world. Embrace the artistic side of science, and you'll find new ways to see and understand reality.

The Concept of "Good Taste" in Science

Following what you like in your research means following your sense of aesthetics, your taste. So, what does it mean to have “good taste”?

In short, someone with good taste tends to follow their intuition to discover useful theories that make accurate and testable predictions. Someone with bad taste tends to follow their intuition to theories that make incorrect predictions or, even worse, no concrete predictions at all.

But, that's oversimplified of course. Perhaps we should add another axis, the axis of conformity (conventional vs. unconventional taste).

Good vs. Bad Taste

• Good Taste: A person has good taste if the models and theories they find beautiful and intuitive are also those that consistently make accurate predictions and work well in practice. This indicates a deep alignment between their aesthetic intuition and the empirical reality of the phenomena they study.
• Bad Taste: Conversely, a person has bad taste if the theories they find aesthetically pleasing and intuitive fail to make accurate predictions or lack predictive power altogether. This misalignment suggests that their intuitive sense of beauty in scientific models does not correlate well with the actual workings of the natural world.

Conventional vs. Unconventional Taste

• Conventional Taste: A person with conventional taste in science appreciates models and theories that are widely regarded as elegant and beautiful by the broader scientific community. Their sense of beauty and intuition aligns with the mainstream views, making their preferences easily recognizable and often widely accepted.
• Unconventional Taste: A person with unconventional taste in science finds beauty and elegance in models that may not be widely appreciated or accepted by the scientific community. Their preferences might be seen as eccentric or avant-garde, but this does not necessarily diminish the potential validity or usefulness of their theories.

Practical Considerations

1. Cultivating Good Taste: To cultivate good taste in science, individuals should focus on honing their intuition through deep study of fundamentals, active experimentation, and reflective practice. Engaging with a wide range of theories and seeking to understand why successful models work can enhance one's ability to develop effective and beautiful theories.
2. Embracing Unconventional Ideas: Encourage the exploration of unconventional models and theories. While these may not always align with mainstream views, they can provide fresh insights and drive scientific progress in unexpected directions.
3. Balancing Subjectivity and Objectivity: Maintain a balance between subjective aesthetic judgments and objective empirical validation. This balance is crucial for ensuring that intuitive and beautiful models are also useful.

That's why I say science is about practical creativity. I'm the end, it doesn't matter if you really like your theory, or if you have fun working on it, if it's wrong. You need to search for the intersection of beautiful and useful.

I always liked the way Feynman expressed this idea when asked about his Nobel prize, “The prize is in the pleasure of finding the thing out, the kick in the discovery, the observation that other people use it--those are the real things, the honors are unreal to me.”

Challenges of Collaborating Across Philosophies

In both art and science, collaboration plays a vital role. The exchange of ideas between individuals with different tastes and intuitions can lead to innovative solutions and new perspectives. Just as artists might collaborate on a mural, scientists often work in teams, combining their strengths and insights to tackle complex problems.

While my philosophy of science, which emphasizes intuition, aesthetic beauty, and the simplification of complex ideas, offers many benefits, it is not without its challenges. One significant difficulty is collaborating with individuals who hold very different scientific philosophies. The relationship between Richard Feynman and Murray Gell-Mann serves as a poignant example. Although they collaborated early in their careers, their differing approaches eventually led to tension. Gell-Mann criticized Feynman for spending too much time creating anecdotes about himself and focusing excessively on being original and clever, but it was exactly Feynman’s rebelliousness that made him successful.

This kind of philosophical clash can make collaboration challenging. I have experienced similar difficulties in my own work. Over the years, I've encountered many other scientists who, despite their brilliance and the high regard I have for them, were seemingly impossible for me to collaborate with effectively because their approach to science differs so fundamentally from mine. They may prioritize rigorous, methodical analysis over intuitive leaps, or they may value empirical data collection over the aesthetic and theoretical elegance of a model. We may just have a different definition of “good taste”.

Even among those who share the same philosophy of science, differences in intuition and perceptions of simplicity can lead to disagreements and challenges in collaboration. Simplicity, much like beauty, is subjective. What one person considers a straightforward approach may appear complex to another. This subjectivity can create friction, even when everyone involved has the same overarching goals and values in their scientific pursuits.

These differences can lead to misunderstandings, conflicts, and a lack of synergy. Neither point of view is necessarily right or wrong. But, not all collaborations are destined to be successful, and sometimes, it is more productive to work independently or with those who share a similar scientific philosophy.

Here are some tips I've found useful for artistic collaboration with other scientists.

The Artist Needs to Create the Prototype Themselves.

Artists and engineers who are collaborating should usually take a divide-and-conquer approach to collaboration so that they are free to pursue their own styles by taking on chunks of a larger project, limiting times of conflict to predefined attempts to merge workstreams. A good way to go this is for one person to take on the role of artist and to build a prototype, and the other person(s) to take on the role of engineer to help refine the prototype. These could always be the same person, or the roles could rotate.

Role Definition: Clearly define roles within the group, assigning tasks that align with each member's strengths and intuitive methods.

Iterative Feedback: Implement an iterative process where ideas are regularly reviewed and explained to the whole group.

Prototyping and Experimentation: Adopt a prototyping mindset where different approaches are tested on a small scale before committing to a single method.

Creative Workshops: Conduct workshops where team members can freely brainstorm and experiment with different approaches without immediate judgment.

Shared Vision: Develop a shared vision or manifesto that encapsulates the group's collective philosophy and goals.

Helping Others Express Themselves

Sometimes you're the writer, and sometimes you're the editor. Make sure it's clear at the outset. If you're the writer, your job is to express your tastes. If you're the editor, your job is to help the writer express their tastes. Not to adopt yours. The biggest mistake collaborators can make is not clarifying who's who at the beginning, especially if you don't have similar tastes.

If you do have similar enough tastes, you and your collaborators may be able to both work together as artists in a way that can be especially rewarding. Personally, I've only found that alignment with a handful of collaborators over my 15 year scientific career, divide and conquer is usually a safer option.

Putting the Art in AI

Artificial Intelligence is evolving like species do. I don't mean that they are a new species. Rather, different computational environments (CPU, GPU, small memory, large memory, etc.), diverse data resources (images, text, tabular, time series), and various selection pressures (loss functions, etc.) create a vast array of AI types, much like biological species in different niches. The researcher’s role is not to discover an ultimate truth or create the perfect AI – such an entity doesn't exist. Instead, the goal is to develop and express personal intuition and tastes through AI research, and to train models that can be useful.

The primary objective for AI researchers is to cultivate a universal and predictive intuition. This means understanding the principles underlying AI behavior in a way that can be broadly applied across different contexts. The secondary goal is to express this intuition by producing tangible artifacts such as formulas, programs, papers, and presentations. These outputs are the researcher’s way of communicating their unique insights and understanding.

Inspiration is key to AI research. It often stems from identifying something that feels off about an existing method, combining two existing ideas in a novel way, or noticing unique characteristics in a dataset. The initial phase of research should focus solely on thinking about the problem. No papers, whiteboards, LaTeX, or code – just pure imagination and visualization. Researchers should try to visualize the algorithm with geometric clarity, simplifying the problem to its core essence.

Go for a walk. Preferably in nature. Or go to a museum. Go to the gym. Lay on the couch and listen to music. Go out at night and look at the stars.

Writing thoughts on paper or whiteboards and drawing diagrams helps clarify and refine ideas. Stripping the problem down to its essence is crucial, avoiding any unnecessary complexity. This simplified approach ensures that the core elements of the problem are addressed without distractions.

Discussions with colleagues, though limited to small groups of up to three people, are vital. This collaboration helps hone intuition, but it’s essential to remember that the final idea is a personal expression of the researcher’s intuition. Pleasing others is not the objective. It doesn’t matter if they don’t get it as long as you get it and, in the end, it works.

The development process should be iterative. Researchers should repeat the initial steps until they feel ready to move on, whether that takes hours or months. Sitting with an idea for an extended period and still feeling confident about it is a good sign of its robustness. Don’t move on prematurely. The work moves at the pace it moves.

Creating a toy problem that retains all essential elements but nothing else is the next step. This simplified problem provides a concrete and manageable testing ground for the initial model.

Coding should begin with a quick, rough draft, accompanied by extensive comments to describe the intuition behind the code. Moderate code hygiene and version control are essential though, even in the early stages, or you'll regret it later. Simple baselines should be included to ensure they work before experimenting with the model.

Experimentation should be incremental, with changes made one at a time to observe their effects. Researchers should aim to predict the impact of changes using their intuition, further simplifying the model if possible. If results are unsatisfactory or the process deviates significantly from the starting point, it’s crucial to return to the beginning and refine your intuition further.

Only after fully understanding and feeling confident in the simpler cases should scale or complexity be added. Detailed notes in LaTeX, along with diagrams explaining the model for different audiences, help in thoroughly documenting the intuition and model. The code should be rewritten, focusing on clarity, minimal abstractions, and extensive testing on both toy and real problems.

To add structure to this creative and iterative process, consider the following principles from practical machine learning research:

1. Build the baseline first: Start with a simple method to establish a benchmark. This provides a comparison point for new methods and helps develop an initial understanding of the problem.
2. Do things that don’t scale: Initially, focus on rapid, iterative experimentation without worrying about scalability. This helps develop intuition before committing to more complex implementations.
3. Hone your physical intuition: Engage deeply with the problem, thinking through results and iterating until something clicks. Imagine it, visualize it, rather than reason through it. This intuitive understanding guides effective experimentation.
4. Get rid of things that don’t work: Regularly clean up and remove non-working methods to avoid biases and streamline future experiments. Focus on refining what works.

Optimization of the model’s performance should be approached as post-production, fine-tuning details after establishing a deep understanding. If intuition fails at any point, revisiting the start is necessary. The final step is writing a comprehensive paper to share the developed intuition, focusing on personal expression rather than conforming to specific journal requirements. Sharing the work, both internally and publicly, is important, but the primary goal is to express and communicate the researcher’s unique insights.

By blending these structured principles with the artistic and intuitive approach to AI research, researchers can navigate the challenges of both fundamental and applied work, ultimately contributing meaningful and innovative solutions to the field.

Balancing Aesthetics with Practical Results

Although driven by a sense of aesthetics, taste, and intuition in research, the ultimate goal remains to create something that works effectively. This pursuit of functionality within defined timeframes does not inherently contradict the reliance on intuition. Confidence in one's taste is crucial; the belief that what resonates aesthetically will also perform well is powerful. Thus, following intuition and personal taste can serve as a reliable proxy for developing successful solutions.

To achieve this balance, it is helpful to engage in cycles of exploration and exploitation. During the exploration phase, the focus is on artistic self-expression and the development of intuition. This period is not necessarily about producing tangible results but about honing one's understanding and feeling for the problem. It is a time for free-form thinking, experimentation, and creativity without the pressure of immediate practical application.

In contrast, the exploitation phase involves leveraging the refined intuition from the exploration phase to build concrete applications. This phase is about "getting shit done," focusing on shipping functional products and achieving measurable outcomes. The insights gained during exploration are put to practical use, ensuring that the aesthetic and intuitive elements translate into effective solutions.

Interestingly, new ideas often start to form during the exploitation phase. Write them down and let them marinate awhile. This subconscious processing allows for the next wave of exploration to begin while still completing the current project. This feeling of having the next idea "waiting in the wings" provides a sense of continuity and motivation. It ensures that while the focus is on practical application, the creative and intuitive process is continuing.

By alternating between exploration and exploitation phases, researchers can maintain a balance between artistic expression and practical results. This cyclical approach ensures that intuition and aesthetics are always aligned with the end goal of creating functional, impactful AI solutions.

Programming as a Craft

Finally, let's talk about craft.

Writing good code is not just about achieving the intended functionality within computational constraints; it is also about simplicity, intuitiveness, and beauty. From the overall architecture to variable names, the act of writing code is a deeply personal experience.

A well-crafted codebase is a reflection of the programmer's mind. It reveals their thought process, problem-solving approach, and attention to detail. Just as a painter considers each brushstroke, a programmer meticulously selects every function, method, and class to construct a coherent and elegant solution. This process transforms programming from a mere technical task into an act of self-expression.

Simplicity is a hallmark of beautiful code. Stripping down the complexity to its essentials allows the core functionality to shine. Simple code is easier to understand, maintain, and extend. It communicates its purpose clearly, leaving no room for ambiguity. Achieving simplicity often requires a deep understanding of the problem and the willingness to refine and iterate on solutions until the essence is captured perfectly.

Intuitive code is another key aspect of programming aesthetics. Code should be written in a way that others (especially your future self) can read and grasp its intent effortlessly. This involves using meaningful variable names, clear logic, and consistent styling. Simplicity. Intuitive code fosters collaboration, enabling teams to work together seamlessly and build upon each other’s work without unnecessary friction.

Beauty in code also lies in its structure. The architecture of an application should be well-organized, modular, and scalable. But, it also shouldn't try to do too much. Doing too much is the programmer's downfall. Each component should have a clear role, and dependencies should be minimized to reduce complexity. A beautifully structured codebase is not only a pleasure to work with but also more resilient to changes and easier to debug.

When programmers pour their passion and creativity into their code, they elevate their work beyond mere functionality. They craft something that resonates on a deeper level, showcasing their skills and aesthetic tastes. This act of creating beautiful code is an embodiment of the programmer’s dedication to their craft, much like an artist dedicates themselves to their masterpiece.

Conclusion

Intuition. Simplicity. Creativity. Experimentation. Iteration. Imagination. Craft. Aesthetics. Taste.

In my opinion, these are the ingredients to great science. The keys to making new discoveries. Therefore, the path of the scientist is more like that of an artist than one ruled by logic, data, and analysis. That's what I believe. And as usual, someone already said it better than I can.

“I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge. For knowledge is limited, whereas imagination encircles the world."

--Albert Einstein

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