[Paper Review] Scientific notations for the digital era

Konrad Hinsen|arXiv (Cornell University)|May 10, 2016

Scientific Computing and Data Management12 references3 citations

TL;DR

This paper argues that digital scientific knowledge—expressed through programming languages and data formats—suffers from poor human usability despite its computational efficiency. It proposes designing simplified, flexible, and interoperable formal languages as digital scientific notations, enabling scientists to express, compose, and share computational knowledge meaningfully, with examples from Lisp/Racket and MOSAIC illustrating practical frameworks for such notations.

ABSTRACT

Computers have profoundly changed the way scientific research is done. Whereas the importance of computers as research tools is evident to everyone, the impact of the digital revolution on the representation of scientific knowledge is not yet widely recognized. An ever increasing part of today's scientific knowledge is expressed, published, and archived exclusively in the form of software and electronic datasets. In this essay, I compare these digital scientific notations to the the traditional scientific notations that have been used for centuries, showing how the digital notations optimized for computerized processing are often an obstacle to scientific communication and to creative work by human scientists. I analyze the causes and propose guidelines for the design of more human-friendly digital scientific notations.

Motivation & Objective

• To highlight the inadequacy of current digital scientific notations—such as programming languages and file formats—for human-centered scientific communication and creative research.
• To argue that computational science should be treated with the same scrutiny as experimental and theoretical work, requiring peer review of software and digital representations.
• To advocate for the design of digital scientific notations that are simple, flexible, and interoperable, modeled on formal languages rather than traditional software or data formats.
• To address the artificial dichotomy between software and data in scientific computing by unifying them under a common formal language framework.
• To encourage computational scientists to rethink digital knowledge representation not as file formats or code, but as expressive, human-readable notations for scientific reasoning.

Proposed method

• Use formal languages from computer science as a unifying foundation for digital scientific notations, treating both data formats and programming languages as instances of the same concept.
• Propose a layered architecture: basic data types (numbers, arrays, trees, maps) at the lowest level, with standardized, lossless interconversion between bit representations (e.g., XML, HDF5, IPFS).
• Enable language extensibility and composition via modular language design, exemplified by Racket’s language framework, where new languages can inherit from and extend existing ones.
• Introduce domain-specific notations built on a common core, such as MOSAIC for molecular simulations, using generic data structures and multiple bit-level representations.
• Leverage existing standards like OpenMath content dictionaries for mathematical expressions and support interoperability through well-defined interfaces.
• Prioritize human usability by ensuring languages are small, memorizable, and extensible to individual and community needs, avoiding the complexity of full programming languages.

Experimental results

Research questions

• RQ1 Why are current programming languages and data formats inadequate as vehicles for scientific communication despite their computational efficiency?
• RQ2 How can digital scientific notations be designed to support both human understanding and machine processing in computational science?
• RQ3 What structural and semantic properties must a digital notation possess to enable reliable composition of scientific knowledge across different tools and domains?
• RQ4 To what extent can formal languages serve as a unified interface between scientists and computational systems, replacing the current fragmented approach to software and data?
• RQ5 How can interoperability between diverse digital scientific notations be achieved without sacrificing simplicity or flexibility for individual researchers?

Key findings

• Digital scientific notations based on programming languages and file formats are optimized for computers but hinder human understanding and creative scientific work.
• The distinction between software and data in computational science is artificial and not reflected in the structure of scientific knowledge, leading to poor integration and communication.
• Formal languages provide a unifying foundation for digital scientific notation, enabling both machine processing and human readability when designed with simplicity and extensibility in mind.
• The Racket language framework demonstrates that small, composable, and interoperable languages can be built and extended easily, supporting both research and software development.
• Interoperability is achievable through standardized, lossless conversion between bit representations (e.g., XML, HDF5, IPFS), even when multiple formats coexist.
• Existing efforts like MOSAIC show promise but fall short due to lack of a shared foundational layer of data types, underscoring the need for a common core to enable broader reuse and composition.