The model for this work was the description of the physical world by mathemati- cal laws. It were always the simplest phenomena which were treated by this scientific method. Physicists studied simple motions inorder to find the mathematical laws. Astronomists observed the orbits of planets in order to find the laws of gravity. One of the simplest measurable phenomenon in the brain is the stimulus- response task. Suchtasks have beenknown since the lastcentury bypsychiatrists and psycholo- gists (v. Helmholtz). There existsa vast literature about the measurement and theory of simple reaction tasks and various choice reaction tasks, visualor auditory. They have beenmeasured and havebeendescribedmathematically.One of the firstmodels for the reaction times used a logarithmic function. But many intriguing questions remained open aboutreaction tasks especiallythe neural explanation ofthe findings. The new tool to investigate the neural structure of stimulus-response sequences was the computer.
Now it was possible to measure the reaction times by using spe- cial programs, to compute the elementary times and the pathway structures from these reaction times, to evaluate the results statistically, to simulate the results, and to write this text. It was this instrument which permitted to save large amounts of data and evaluate them by special software written for this purpose. Thus it was possible to compute the time quanta and the pathways and to understand each re- action time as an integer multiple of this time quantum (plus a constant value).
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I The time measurement of stimulus-response pathways.- Measurement of reaction times in healthy subjects.- Bihemispheric visual reaction tasks.- Summary.- Methods.- Subjects.- Tasks.- Apparatus.- Procedure.- Design.- Data analysis.- Comparison of the computer program with a standard device.- Results.- Illustration of linear relationship between the number of basic elements (stimuli and responses) and the mean reaction time.- Fundamental data.- The time differences between the tasks.- The quotient (v(N+l)(N+l) ? vNN)/slope.- The quotient (v(N+l)(N+l) ? vNN)/dvCT.- Beyond the end of sequential processing (ESP): the begin of parallel processing.- Bihemispheric visual intermediate reaction tasks.- Minimal reaction times (also linear growing with number of alternatives).- Direct observation of the cycle time and comparison with the computed cycle time values.- Discussion.- Discussion of the method.- Comparison of the linear with the logarithmic relation.- Comparison with reaction times given by other authors.- Some theoretical considerations.- Minimal visual reaction time.- Brain imaging of reaction task pathways.- A first mathematical theory of bihemispheric visual reaction tasks.- Fundamentals.- Implicit learning may decrease the number of cycles.- Can the number of cycles be reduced furthermore?.- The bihemispheric visual median finger reaction tasks.- Summary.- Method.- Results.- Each finger yields similar reaction times when tapping at the same key.- Each finger yields different reaction times within the tasks v99 or vlOlO.- The median finger reaction time of a specific finger has its own slope from the task vll to the task vlOlO.- Discussion of the bihemispheric visual median finger reaction times.- The discrepancy between the finger reaction times in the tasks v99 and vll and the reaction time for each single finger in the tasks vllLLF etc.- Is cycle time or cycle number responsible for different finger reaction times?.- Observing or computing the different cycle numbers?.- The line of the median reaction times is the mean of the lines of median finger reaction times.- Monohemispheric visual reaction tasks.- Summary.- Method.- Examples of monohemispheric visual reaction tasks.- Direct observation of visual cycle times.- Direct observation of visual cycle numbers.- Results.- The monohemispheric visual median reaction times.- The monohemispheric visual median finger reaction times.- The directly observed cycle times in monohemispheric visual reaction tasks (v22y).- The directly observed cycle number in monohemispheric visual reaction tasks.- The number of cycles in monohemispheric visual reaction tasks computed by dvCT.- The intercepts of monohemispheric visual reaction tasks.- The number of cycles in monohemispheric visual reaction tasks computed by dvCTy.- Discussion.- The reason of the asymmetry between the two monohemispheric visual pathways v22l and v22r.- Why is the mean cycle number reduced in some fingers (n>4) and in some sides?.- Monohemispheric auditory reaction tasks.- Method.- Collecting the data.- Evaluating the data.- Results.- The monohemispheric auditory median reaction times.- The monohemispheric auditory median finger reaction times.- The directly observed cycle times in monohemispheric auditory reaction tasks (a221 and a22r).- The directly observed cycle numbers in monohemispheric auditory tasks.- The computed number of cycles in monohemispheric auditory reaction tasks.- The intercepts of monohemispheric auditory reaction tasks.- Implicit learning in monohemispheric auditory reaction tasks.- Discussion of monohemispheric auditory reaction tasks.- The hypothetical structure of the task a22y.- Empirical evidence.- Comparison of the directly observed auditory and visual cycle times.- Discussion of auditory and visual cycle times.- Discussion of cycle times of lower areas (sensory or motor).- Discussion of auditory and visual decision times.- Does the right hemisphere decide the visual tasks and the left hemisphere the auditory tasks?.- The monohemispheric cycle times are nearly independent from the target key.- The intra-individual variability of reaction time.- Method.- Results.- Reduction of directly observed cycle numbers in subjects.- Discussion.- Preliminary remark.- Reduction of cycle numbers in various tasks after full implicit learning.- Measurement of reaction times in patients.- The reaction times of patients with monohemispheric brain lesions.- The reaction times of patients with schizophrenia.- Methodical adaptions.- Graphical presentation of different influences on reaction time.- The event-related potentials of reaction tasks.- The ERP of auditory reaction tasks.- The subtraction potentials.- The neural correlates of positive and negative evoked potentials.- The knowledge from PET and fMNR about the neural correlates of auditory reaction tasks.- The correlation between the latencies of the single potentials and the structure of the task all.- II The spatiotemporal structure of stimulus-response pathways.- Measurement of elementary time.- The procedure "NESTLE" in a computer program called "FPM31e".- The NESTLE procedure applied to a 5 millisecond time scale of reaction times (program FPM31e, procedure NESTLE).- The NESTLE procedure applied to a 1 millesecond scale of reaction times (program FPM26f58).- Application of the NESTLE procedure of FPM to all tasks of a subject.- Convergence of the results of FPM31e, FPM26f58, and chronophoresis.- Problems.- The confrontation of FPM with artificial data.- The Chronophoresis of xlly, x22y, and x33y.- The NESTLE procedure applied to a set of reaction times (program SINGLE).- The chronophoresis of xlly gives better results than that of x22y or x33y.- Difficulties in distinguishing between certain elementary times.- The difference between SINGLE104r and SINGLE106n.- Artificial data.- Attributes of elementary times.- The intra-individual stability of elementary times.- The symmetry of elementary times.- Measurement of pathway structure.- The linear and cyclical part of the pathway (FPM31e).- The elementary times ET(aNNr), ET(aNNl), ET(vNNr), ET(vNNl).- The input time and the output time are summed up to the constant time (CON).- The first peak, FP, of a reaction time distribution is an indicator for the minimal pathway.- (Fp-2ET) divides the linear from the cyclical part in minimal stimulus-response pathways.- The median reaction time MEDIAN.- linEN=(Fp-con)/ET-2 is the number of elementary times in the linear part of the minimal pathway.- cycEN=(Median-Fp)/ET-2 is the number of elementary times between the linear part of the minimal pathway and the median length of the pathway.- Example of the NESTLE results and the reaction times distribution of one task.- Pathway information from the lms-distribution (FPM26f58).- Simulation of a reaction time distribution using the program SIMxl ly.- Hypothetical neural representation.- The cortical structure of the sensory portion of the visual pathway.- Hypothetical division of the stimulus-response pathway into a linear and a cyclical part.- The structure (equation) of mental pathways.- Minimal pathway.- Median pathway.- The variability of the linear part of the pathway.- The variability of the linear pathway within one task (with 100 trials).- The variability of the linear pathway in a rapid succession of tasks.- Subject H23E.- The variability of the linear pathway due to experimental distractions.- Empirical investigations how certain distractions influence the task vllrH23.- Hypothetical interactions between two tasks.- The delay of the task vllr caused by the nFT task of the left hand correlates with the number of tapping fingers.- The variability of the linear pathway in repetitions of tasks after days to months.- The variability of the linear pathway in single trials of event-related potentials (ERP).- The neural representation of variations of the linear pathway.- Examples of linear pathways of the task xlly.- The cortical structure of the sensory part of the visual pathway.- The cortical structure of the sensory portion of the auditory stimulus-response pathway.- The length of the linear portion and the attentional state.- Why should the linear pathway be constant in a task with 100 trials?.- Do the lengths of the linear pathways in one series of a subject change homogeneously (with the same difference) compared to a subsequent series?.- The variability of the cyclical part of the pathway.- Requirements.- The minimal cyclical pathway.- The median cyclical pathway depends on the mode and the number of searching sets.- The difference between the internal mean, the external mean, and the external observable median number of searching cycles.- The mathematical structure of mental pathways.- The irreversibility of the searching mode (the implicit learning axiom).- The reversibility of the number of searches in xlly and x22y.- Examples of pathways.- The subject 013A.- The evaluation of vl lrHOlC.- The evaluation of vlly
