The paper explores the difference between diagrammatic and sentential representations in problem-solving, particularly in mathematics and physics. It argues that diagrams can be more efficient than sentences for solving problems because they organize information spatially, making it easier to find and use. Diagrams allow for direct access to information and can guide problem-solving through a smooth traversal of the diagram, reducing the need for extensive search or computation. This is in contrast to sentential representations, which are sequential and require more effort to locate and process information. The paper contrasts the computational efficiency of diagrammatic and sentential representations, noting that diagrams can support more efficient search and recognition processes. Diagrams preserve topological and geometric relations between components, while sentential representations may only preserve temporal or logical sequences. The paper also discusses how diagrams can facilitate recognition by making implicit information explicit, which is crucial for tasks like geometry proofs. The paper provides examples of both representations, including a pulley problem and a geometry problem. In the pulley problem, the diagrammatic representation allows for faster and more efficient problem-solving, as it reduces the need for extensive search and labeling. In the geometry problem, the diagrammatic representation also reduces search and labeling requirements, but the given data structure does not match the given program, requiring enhancements to the data structure and program to solve the problem. The paper concludes that diagrams can be more efficient than sentences for problem-solving, particularly in domains where spatial relationships are important. It also highlights the importance of matching the representation to the problem and the need for appropriate inference rules and attention management systems to ensure effective problem-solving.The paper explores the difference between diagrammatic and sentential representations in problem-solving, particularly in mathematics and physics. It argues that diagrams can be more efficient than sentences for solving problems because they organize information spatially, making it easier to find and use. Diagrams allow for direct access to information and can guide problem-solving through a smooth traversal of the diagram, reducing the need for extensive search or computation. This is in contrast to sentential representations, which are sequential and require more effort to locate and process information. The paper contrasts the computational efficiency of diagrammatic and sentential representations, noting that diagrams can support more efficient search and recognition processes. Diagrams preserve topological and geometric relations between components, while sentential representations may only preserve temporal or logical sequences. The paper also discusses how diagrams can facilitate recognition by making implicit information explicit, which is crucial for tasks like geometry proofs. The paper provides examples of both representations, including a pulley problem and a geometry problem. In the pulley problem, the diagrammatic representation allows for faster and more efficient problem-solving, as it reduces the need for extensive search and labeling. In the geometry problem, the diagrammatic representation also reduces search and labeling requirements, but the given data structure does not match the given program, requiring enhancements to the data structure and program to solve the problem. The paper concludes that diagrams can be more efficient than sentences for problem-solving, particularly in domains where spatial relationships are important. It also highlights the importance of matching the representation to the problem and the need for appropriate inference rules and attention management systems to ensure effective problem-solving.