Julien Gori
Olivier Rioul
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Abstract
The rationale for Fitts’ law is that pointing tasks have the information-theoretic analogy of sending a signal over a noisy channel, thereby matching Shannon’s capacity formula. Yet, the currently received analysis is incomplete and unsatisfactory: There is no explicit communication model for pointing; there is a confusion between central concepts of capacity (a mathematical limit), throughput (an average performance measure), and bandwidth (a physical quantity); and there is also a confusion between source and channel coding so that Shannon’s Theorem 17 can be misinterpreted. We develop an information-theoretic model for pointing tasks where the index of difficulty (ID) is the expression of both a source entropy and a zero-error channel capacity. Then, we extend the model to include misses at rate ε and prove that ID should be adjusted to (1−ε)ID. Finally, we reflect on Shannon’s channel coding theorem and argue that only minimum movement times, not performance averages, should be considered.
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Index Terms
- Speed-Accuracy Tradeoff: A Formal Information-Theoretic Transmission Scheme (FITTS)
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