Search

In 1998/1999 three participants trained for up to 74 hour long sessions to find a target in visual displays of 1, 2, or 4 objects. There were four targets and four foils that never changed. Displays occurred simultaneously, or the objects occurred successively, or the features of each object occurred successively. When successive, the SOAs were short (17, 33, or 50 ms) so the displays appeared simultaneous, making it likely that the search strategy was the same in all conditions. A 2004 publication examined only the simultaneous condition and found evidence for serial search as well as some small amount of automatic attention to targets, and occasional early or late search termination. A 2021 publication examined only the displays with single objects, obtaining evidence for dynamic perception of features. Building on these results we present a simple dynamic model that explains the main processes operating in all the experimental conditions.

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We argue that depending on p-values to reject null hypotheses, including a recent call for changing the canonical alpha level for statistical significance from .05 to .005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable criterion levels both are problematic, it is sensible to dispense with significance testing altogether. There are alternatives that address study design and determining sample sizes much more directly than significance testing does; but none of the statistical tools should replace significance testing as the new magic method giving clear-cut mechanical answers. Inference should not be based on single studies at all, but on cumulative evidence from multiple independent studies. When evaluating the strength of the evidence, we should consider, for example, auxiliary assumptions, the strength of the experimental design, or implications for applications. To boil all this down to a binary decision based on a p-value threshold of .05, .01, .005, or anything else, is not acceptable.

TLA+ is a specification language based on standard set theory and temporal logic that has constructs for hierarchical proofs. We describe how to write TLA+ proofs and check them with TLAPS, the TLA+ Proof System. We use Peterson's mutual exclusion algorithm as a simple example to describe the features of TLAPS and show how it and the Toolbox (an IDE for TLA+) help users to manage large, complex proofs., A shorter version of this article appeared in the proceedings of the conference Formal Methods 2012 (FM 2012, Paris, France, Springer LNCS 7436, pp. 147-154)