Laughing at Numbers: Evidence for Numeracy in the “Philogelos”

Ancient numeracy is reasonably well attested in scientific sources. However, any study of applied mathematics faces the problem of a dearth of evidence. The paper suggests that the jokes collected in the “Philogelos” provide such evidence, and discusses the failings which are referred to in these jokes.Ancient numeracy is reasonably well attested in scientific sources. However, any study of applied mathematics faces the problem of a dearth of evidence. The paper suggests that the jokes collected in the “Philogelos” provide such evidence, and discusses the failings which are referred to in these jokes

DIE SICHERUNG EINES ANTIKEN STADTTORS BEI AENEAS TACTICUS. QUELLE UND MODELLE

Aineias (Aeneas Tacticus) legt in seinen Poliorketika dar, wie im Altertum eine kleine Stadt einer Belagerung standhalten kann. Die Schrift ist das älteste militärische Fachbuch, das uns aus der Antike erhalten ist, und bietet die ausführlichste Beschreibung darüber, wie ein Stadttor gesichert wird. Zur Deutung dieser historischen Quelle sind verschiedene, oft hochkomplizierte Modelle vorgeschlagen worden. Der Aufsatz entwickelt eine dem Text eher entsprechende einfache Deutung. Diese vermeidet es, aus anderen Zeugnissen übertragene oder aber nur mit argumenta e silentio begründete Deutungen zum Verständnis des Textes einzusetzen, und macht damit nachvollziehbar, weshalb Aineias weniger auf Technik als vielmehr auf das Vertrauen der Bewohnerschaft zueinander setzt, wenn es um die Sicherung einer von Feinden bedrohten Stadt geht, denn, wie Aineias betont, “zuerst muss man zusehen, ob die Bürger einträchtig sind, da dies bei einer Belagerung das höchste Gut ist.

Bäuerliche Zeitvermessung bei Palladius

Der spätantike Autor Palladius bietet in seinem Opus Agriculturae Angaben zu den Schattenlängen am Ende jeder Stunde in jedem Monat und ermöglicht dem Landwirt so, zum rechten Zeitpunkt zu agieren. In der Forschung wurde bisher vergeblich versucht, das System von Palladius' Zeitmessung nachzuvollziehen, die Herkunft der Angaben zu erweisen oder sie gar als Beleg für die Heimat des Autors zu deuten. Der Aufsatz schlägt eine neue Interpretation für die Berechnung der Schattenlängen bei Palladius und für ihre Nutzung vor: die Anwendung von Prinzipien der Land- für die Zeitvermessung.The late antique writer Palladius provides in his Opus Agriculturae shadow lengths at the end of every hour and every month, allowing the farmer to act at the right time. Previous research has attempted in vain to understand the system of Palladius' calculations, to prove the origin of the information or even to interpret it as evidence for the provenance of the author. The paper proposes a new interpretation for the calculation of the length of the shadows in Palladius and for their use: the application of principles of land surveying to time surveying

Atypical processing of uncertainty in individuals at risk for psychosis

Current theories of psychosis highlight the role of abnormal learning signals, i.e., prediction errors (PEs) and uncertainty, in the formation of delusional beliefs. We employed computational analyses of behaviour and functional magnetic resonance imaging (fMRI) to examine whether such abnormalities are evident in clinical high risk (CHR) individuals. Non-medicated CHR individuals (n = 13) and control participants (n = 13) performed a probabilistic learning paradigm during fMRI data acquisition. We used a hierarchical Bayesian model to infer subject-specific computations from behaviour – with a focus on PEs and uncertainty (or its inverse, precision) at different levels, including environmental ‘volatility’ – and used these computational quantities for analyses of fMRI data. Computational modelling of CHR individuals’ behaviour indicated volatility estimates converged to significantly higher levels than in controls. Model-based fMRI demonstrated increased activity in prefrontal and insular regions of CHR individuals in response to precision-weighted low-level outcome PEs, while activations of prefrontal, orbitofrontal and anterior insula cortex by higher-level PEs (that serve to update volatility estimates) were reduced. Additionally, prefrontal cortical activity in response to outcome PEs in CHR was negatively associated with clinical measures of global functioning. Our results suggest a multi-faceted learning abnormality in CHR individuals under conditions of environmental uncertainty, comprising higher levels of volatility estimates combined with reduced cortical activation, and abnormally high activations in prefrontal and insular areas by precision-weighted outcome PEs. This atypical representation of high- and low-level learning signals might reflect a predisposition to delusion formation

Valid population inference for information-based imaging: From the second-level t-test to prevalence inference

In multivariate pattern analysis of neuroimaging data, ‘second-level’ inference is often performed by entering classification accuracies into a t-test vs chance level across subjects. We argue that while the random-effects analysis implemented by the t-test does provide population inference if applied to activation differences, it fails to do so in the case of classification accuracy or other ‘information-like’ measures, because the true value of such measures can never be below chance level. This constraint changes the meaning of the population-level null hypothesis being tested, which becomes equivalent to the global null hypothesis that there is no effect in any subject in the population. Consequently, rejecting it only allows to infer that there are some subjects in which there is an information effect, but not that it generalizes, rendering it effectively equivalent to fixed-effects analysis. This statement is supported by theoretical arguments as well as simulations. We review possible alternative approaches to population inference for information-based imaging, converging on the idea that it should not target the mean, but the prevalence of the effect in the population. One method to do so, ‘permutation-based information prevalence inference using the minimum statistic’, is described in detail and applied to empirical data