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Wiener’s Anti-Aircraft Cannon
In his autobiography, Norbert Wiener explains that at the beginning of the war, many researchers and engineers were looking “ in what sector of work [they] might make [them]selves of use” [162].2 During the war, Wiener worked on improving the design of anti-aircraft cannons, which were tricky to operate effectively. An operator of an anti-aircraft cannon must aim ahead of the plane he is trying to shoot down. The operator is thus faced with a complex task of prediction as the pilot will usually engage in audacious maneuvers to escape the ballistic shell. The design of a “smart” cannon is conditioned by the limits of human motor performance; the plane is controlled by a pilot who can only react so fast and only withstand so many dynamical constraints, and the operator who controls the cannon faces similar constraints. Providing an adequate model for the human and its extreme performance thus proved essential, and collaboration between behavioral psychologists and engineers was therefore required —although Wiener would ultimately propose a solution that would remove the human completely out of the loop. Wiener adapted results from integral equations he had developed some time before to solve the prediction problem; this solution was then used to control the cannon using feedback to avoid modeling too precisely the cannon itself: “ Not only is a feedback system less dependent on changes of load than a system without feedback, but this dependence becomes increasingly less as more and more motion is fed back” [162]. Wiener noticed that when the feedback was too strong, his system would start to oscillate wildly and uncontrollably i.e., would become unstable. Wiener made a parallel between human controlled movement and servo-mechanisms, which already implemented feedback at the time and asked a neurophysiologist, Dr Rosenblueth, whether humans could also display signs of instability. Rosenblueth informed him of intention tremors; wild uncontrolled oscillations that would perturb simple tasks, such as grasping a glass of water, but would be unapparent at rest. From this point, Wiener would see the human nervous systems as a complex system made up of multiple feedback loops; and he would eventually analyze many other fields such as economics, politics, sociology with the same scrutiny [161, 163].
Macy Conferences and Cybernetics
Six months after the end of World War II, a set of conferences was initiated by the Macy Foundation that came to be known as the Macy Conferences with the following goal: 3 To make best use of our time, we will ask that the themes be discussed so as to make known theoretical and practical developments in the domains of computing machines and apparatuses that aim for their targets, and in each case exemplifications in physiology should be presented. After, we will consider problems of psychosomatic, psychological, psychiatric and sociological nature where these notions are applicable and we will see which extensions of the theories are necessary for these issues. These conferences would gather, among others, Wiener (mathematician, “father of cybernetics”, known for his work on Fourier transforms and Brownian motion), Von Neumann (mathematician)4 , Shannon (mathematician, “father of information theory”, also known for applying Boolean logic to electrical circuits design and work on cryptography), Bar-Hillel (mathematician and linguist), Bateson (linguist and anthropologist), Bigelow (engineer who had worked with Wiener on the anti-aircraft gun), Hutchinson (“father of modern ecology”), Lewin (psychologist), Licklider (psychologist and computer scientist), Luce (mathematical psychologist), MacKay (physicist, known for his work on the theory of brain organization), McCulloch (neurophysiologist), Morgenstern (economist), Pitts (logician), Quastler (radiologist), Wiesner (electrical engineer), Young (zoologist and neurophysiologist). A sample of the topics discussed throughout the Macy conferences (1946–1953) illustrates the diversity of the talks delivered:
Self-regulating mechanisms,
Anthropology and how computers might learn,
Perceptual effects of brain damage,
Analog versus digital approaches to psychological models,
Memory,
Reaction from the Communication Engineers
The use of information theory outside the sphere of communication engineering was challenged by the information theory community, and Shannon himself. In a famous editorial, Shannon [133] expressed the view that information theory “has perhaps been ballooned to an importance beyond its actual accomplishments.” He also insisted that “the use of a few exciting words like information, entropy, redundancy, do not solve all our problems.” Tribus [90, p. 1] reports a private conversation he had with Shannon who “made it quite clear that he considered applications of his work to problems outside of communication theory to be suspect and he did not attach fundamental significance to them”. Elias [30], an important figure of the information theory society to which we will return in Chapter 6, urged authors—using a very ironic, even aggressive tone—to stop writing approximative papers that abused information theoretic results and concepts. Fitts’ work, based on a loose analogy with Shannon’s Theorem 17, is a good example of abuse of information theory:
Why should D/W of Fitts’ law be analogous to P=N as defined in Shannon’s Theorem 17?
What is the bandwidth BW of Shannon’s Theorem 17 analogous to in Fitts’ law ? There seems to be no reason to identify BW to 1=MT beyond the fact that both are expressed in the same physical units (s1).
Since D and W are amplitudes while P and N are powers, what happened to the squares10 ?
Table of contents :
I Preliminaries
1 Shannon’s Information Theory, Psychology, and HCI
1.1 Post-war Cybernetics
1.1.1 Wiener’s Anti-Aircraft Cannon
1.1.2 Macy Conferences and Cybernetics
1.1.3 Annus Mirabilis: 1948
1.2 Psychologists Discover Information Theory
1.2.1 Miller and Frick’s Statistical Behavioristics
1.2.2 Fitts’ Law
1.3 Whatever Happened to Information Theory in Psychology ?
1.3.1 Reaction from the Communication Engineers
1.3.2 Reactions from Psychologists
1.3.3 Fitts’ Law is Not Information-Theoretic Anymore
1.4 Fitts’ Law, Shannon’s Theory, and Human Computer Interaction
1.4.1 Bringing Fitts’ Law in HCI
1.4.2 Importance of Fitts’ Law for the HCI Community
1.5 Discussion
2 Speed-Accuracy Tradeoff: Empirical and Theoretical Exposition
2.1 Characteristics of Human Voluntary Movements: An Empirical Survey
2.1.1 Variability
2.1.2 Feedback and Feedforward Control
2.1.3 Intermittent and Continuous Control
2.2 Theoretical Models for Voluntary Movement
2.2.1 Early Descriptions: A Two-Component Movement
2.2.2 Crossman and Goodeve’s Deterministic Iterative Corrections (DIC) Model
2.2.3 Schmidt’s Law
2.2.4 Meyer et al.’s Stochastic Optimized Submovements (SOS) Model . 53
2.2.5 Bullock & Grossberg’s Vector-Integration-To-Endpoint (VITE) Model 54
2.2.6 Plamondon & Alimi’s model
2.2.7 Elliott and Colleague’s Two-Component Model
2.2.8 Discussion
3 Fitts’ law: Methods and Controversies
3.1 Regressing Movement Time
3.1.1 Time Metrics
3.1.2 Regression
3.2 Formulation
3.2.1 A Remark on the Equivalence Between Indexes
3.2.2 Fit of the Mackenzie Formulation
3.2.3 Small Values of ID
3.3 Nominal versus Effective Width
3.4 Measuring Performance: Throughput
3.5 Discussion
3.6 Appendix
II Information-Theoretic Models for Voluntary Aimed Movement
4 A Basic Source Model: Aiming is Choosing
5 Feedforward Transmission Model with Bounded Noise: A Formal Information Theoretic Transmission Scheme (FITTS)
5.1 Voluntary Movement as a Transmission Problem
5.1.1 Black-box Model
5.1.2 Model Description
5.1.3 Aiming Without Misses
5.2 Fitts’ law and the Capacity of the Uniform Channel
5.2.1 Uniform Channel Versus the Gaussian Channel
5.2.2 Capacity of the Uniform Channel
5.2.3 Uniform Noise
5.2.4 Analogy with Shannon’s Capacity Formula
5.3 Taking Target Misses into account
5.3.1 Handling Misses
5.3.2 A Compliant Index of Difficulty: ID(« )
5.3.3 Comparison between IDe and ID(« )
5.4 Performance Fronts for Fitts’ law
5.4.1 Fitts’ Law as a Performance Limit
5.4.2 A Field Study Example
5.5 Appendix
6 Feedback Transmission Model with Gaussian Noise: A Feedback Information Theoretic Transmission Scheme (FITTS 2)
6.1 Positional Variance Profiles (PVP)
6.1.1 Computation of PVPs
6.1.2 Conjecture: Unimodality of PVP
6.2 A Model for the Variance-Decreasing Phase
6.2.1 Information-Theoretic Model Description
6.2.2 Bounds on Transmitted Information
6.2.3 Achieving capacity
6.3 Exponential Decrease of Variance: Difficulty, Throughput and Fitts’ law
6.3.1 Local Exponential Decrease of Variance
6.3.2 Local Index of Difficulty id and Throughput
6.3.3 Deriving the Classic Fitts’ law
6.3.4 Interpreting the Intercept
6.4 Discussion
6.5 Appendix
III Leveraging and Validating the Transmission Schemes
7 Datasets
7.1 The Goldberg-Faridani-Alterovitz (GFA) Dataset
7.2 The Guiard-Olafsdottir-Perrault Dataset (G-Dataset)
7.3 The Jude-Guiness-Poor (JGP) Dataset
7.4 The Chapuis-Blanch-Beaudouin-Lafon (CBB) Wild Dataset
7.5 The PD-Dataset (Müller-Oulasvirta-Murray-Smith)
7.6 The Blanch-Ortega (BO) Dataset
8 FITTS 1: Leveraging the Front of Performance
8.1 Parametric Estimation
8.1.1 Exponential Distribution
8.1.2 Exgauss Function
8.1.3 Consistency with Fitts’ Law
8.2 Application to Empirical data
8.2.1 Controlled Data
8.2.2 Data Acquired “in the Wild”
8.2.3 Data Acquired in a Web-based Experiment
8.2.4 Discussion
8.3 Appendix
8.3.1 Principle of Maximum Likelihood Estimation (MLE)
8.3.2 exGauss Distribution MLE
9 FITTS 2: Empirical Validation
9.1 Datasets
9.2 PVP unimodality
9.3 Effects of D, ID, W and instruction on and D
9.3.1 Effects of D, ID and W on the time instant of maximum variance
9.3.2 Effects of D, ID and W on the distance traveled D at time
9.3.3 Effect of instructions on and D
9.3.4 Summary
9.4 Link with kinematics
9.5 Empirical Results for the Second Phase
9.5.1 Exponential Decrease of Standard Deviation
9.5.2 Effects of Task Parameters and Instructions . .
