Developing satellite ground control software through graphical models

This paper discusses a program of investigation into software development as graphical modeling. The goal of this work is a more efficient development and maintenance process for the ground-based software that controls unmanned scientific satellites launched by NASA. The main hypothesis of the program is that modeling of the spacecraft and its subsystems, and reasoning about such models, can--and should--form the key activities of software development; by using such models as inputs, the generation of code to perform various functions (such as simulation and diagnostics of spacecraft components) can be automated. Moreover, we contend that automation can provide significant support for reasoning about the software system at the diagram level

Using Diagrams to Understand Geometry

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73219/1/0824-7935.00062.pd

DISTINGUISHING VISUAL IMAGERY AND SPATIAL REASONING

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73598/1/j.1467-8640.1993.tb00228.x.pd

Bar and Line Graph Comprehension: An Interaction of Top-Down and Bottom-Up Processes

This experiment investigated the effect of format (line vs. bar), viewers’ familiarity with variables, and viewers’ graphicacy (graphical literacy) skills on the comprehension of multivariate (three variable) data presented in graphs. Fifty-five undergraduates provided written descriptions of data for a set of 14 line or bar graphs, half of which depicted variables familiar to the population and half of which depicted variables unfamiliar to the population. Participants then took a test of graphicacy skills. As predicted, the format influenced viewers’ interpretations of data. Specifically, viewers were more likely to describe x – y interactions when viewing line graphs than when viewing bar graphs, and they were more likely to describe main effects and “ z – y ” (the variable in the legend) interactions when viewing bar graphs than when viewing line graphs. Familiarity of data presented and individuals’ graphicacy skills interacted with the influence of graph format. Specifically, viewers were most likely to generate inferences only when they had high graphicacy skills, the data were familiar and thus the information inferred was expected, and the format supported those inferences. Implications for multivariate data display are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/78678/1/j.1756-8765.2009.01066.x.pd

An Extensible User Interface for Lean 4

Contemporary proof assistants rely on complex automation and process libraries with millions of lines of code. At these scales, understanding the emergent interactions between components can be a serious challenge. One way of managing complexity, long established in informal practice, is through varying external representations. For instance, algebraic notation facilitates term-based reasoning whereas geometric diagrams invoke spatial intuition. Objects viewed one way become much simpler than when viewed differently. In contrast, modern general-purpose ITP systems usually only support limited, textual representations. Treating this as a problem of human-computer interaction, we aim to demonstrate that presentations - UI elements that store references to the objects they are displaying - are a fruitful way of thinking about ITP interface design. They allow us to make headway on two fronts - introspection of prover internals and support for diagrammatic reasoning. To this end we have built an extensible user interface for the Lean 4 prover with an associated ProofWidgets 4 library of presentation-based UI components. We demonstrate the system with several examples including type information popups, structured traces, contextual suggestions, a display for algebraic reasoning, and visualizations of red-black trees. Our interface is already part of the core Lean distribution

Misinterpretasi Mahasiswa pada Representasi Histogram dan Box Plot

Mathematical representation is the center of mathematics learning. However, is the student's ability to interpret the form of representation good? In this study, we adapted multiple choice questions from the LOCUS assessment to describe how 30 semesters III students interpreted the bar chart and box plot. The students answered this multiple choice question by including the reasons. The results showed that 50% of the 30 students gave correct responses regarding the boxplot. These fifteen students stated that the box plot cannot be used to calculate a lot of data. However, these 15 students were unable to come up with reasons why the box plot could not be used to calculate a lot of data. The remaining 50% of students stated that other diagrams such as scatter plots, histograms and bar charts cannot be used to calculate a lot of data, but box plots can be used to calculate the amount of data. As many as 40% of students are not able to distinguish a bar chart from a histogram. They assumed that qualitative data could be described using a histogram instead of a bar chart. The results of this study are explained by the dual-process theory

Diagrammatic Reasoning and Modelling in the Imagination: The Secret Weapons of the Scientific Revolution

Just before the Scientific Revolution, there was a "Mathematical Revolution", heavily based on geometrical and machine diagrams. The "faculty of imagination" (now called scientific visualization) was developed to allow 3D understanding of planetary motion, human anatomy and the workings of machines. 1543 saw the publication of the heavily geometrical work of Copernicus and Vesalius, as well as the first Italian translation of Euclid