Biometrics has done damage with levels of R or p or Student’s t. The damage widened with Ronald A. Fisher’s victory in the 1920s and 1930s in devising mechanical methods of “testing,” against methods of common sense and scientific impact, “oomph.” The scale along which one would measure oomph is particularly clear in biomedical sciences: life or death. Cardiovascular epidemiology, to take one example, combines with gusto the “fallacy of the transposed conditional” and what we call the “sizeless stare” of (...) statistical significance. Some medical editors have battled against the 5% philosophy, as did, for example, Kenneth Rothman, the founder of Epidemiology. And decades ago a sensible few in education, ecology, and sociology initiated a “significance test controversy.” But, grantors, journal referees, and tenure committees in the statistical sciences had faith that probability spaces can substitute for scientific judgment. A finding of p <.05 is deemed to be “better” for variable X than p <.11 for variable Y. It is not. It depends on the oomph of X and Y—the effect size, size judged in the light of how much it matters for scientific or clinical purposes. In 1995 a Cancer Trialists’ Collaborative Group, for example, came to a rare consensus on effect size: 10 different studies had agreed that a certain drug for treating prostate cancer can increase patient survival by 12%. An 11th study published in the New England Journal in 1998 dismissed the drug. The dismissal was based on a t-test, not on what William Gosset had called, against Ronald A. Fisher’s machinery, “real” error. (shrink)

Formal spaces have become commonplace conceptual and computational tools in a large array of scientific disciplines, including both the natural and the social sciences. Morphological spaces are spaces describing and relating organismal phenotypes. They play a central role in morphometrics, the statistical description of biological forms, but also underlie the notion of adaptive landscapes that drives many theoretical considerations in evolutionary biology. We briefly review the topological and geometrical properties of the most common morphospaces in the biological literature. In contemporary (...) geometric morphometrics, the notion of a morphospace is based on the Euclidean tangent space to Kendall’s shape space, which is a Riemannian manifold. Many more classical morphospaces, such as Raup’s space of coiled shells, lack these metric properties, e.g., due to incommensurably scaled variables, so that these morphospaces typically are affine vector spaces. Other notions of a morphospace, like Thomas and Reif’s skeleton space, may not give rise to a quantitative measure of similarity at all. Such spaces can often be characterized in terms of topological or pretopological spaces. (shrink)

What is the nature of number systems and arithmetic that we use in science for quantification, analysis, and modeling? I argue that number concepts and arithmetic are neither hardwired in the brain, nor do they exist out there in the universe. Innate subitizing and early cognitive preconditions for number— which we share with many other species—cannot provide the foundations for the precision, richness, and range of number concepts and simple arithmetic, let alone that of more complex mathematical concepts. Numbers and (...) arithmetic, and mathematics in general, have unique features—precision, objectivity, rigor, generalizability, stability, symbolizability, and applicability to the real world—that must be accounted for. They are sophisticated concepts that developed culturally only in recent human history. I suggest that numbers and arithmetic are realized through precise combinations of non-mathematical everyday cognitive mechanisms that make human imagination and abstraction possible. One such mechanism, conceptual metaphor, is a neurally instantiated inference-preserving cross-domain mapping that allows the conceptualization of abstract entities in terms of grounded bodily experience. I analyze how the inferential organization of the properties and “laws” of arithmetic emerge metaphorically from everyday meaningful actions. Numbers and arithmetic are thus—outside of natural selection—the product of the biologically constrained interaction of individuals with the appropriate cultural and historical phenotypic variation supported by language, writing systems, and education. (shrink)

It is now well documented that biology needs morphometrics. Morphometrics can provide useful and often unexpected information about development and growth, functional—especially mechanical—adaptation, and evolutionary difference and relationship. Such studies often apply coordinate data from anatomical landmarks. Recently semi-landmarks and sliding landmarks increase information content, especially of apparently featureless regions . Yet, how we landmark our materials limits the results we get and the questions we ask. Here we show different landmarking schemes leading to different equivalences between specimens and different (...) results. Geometric morphometric methods often treat landmarks as points on rubber sheets. Distortions of the sheets are often visualized by techniques like thin plate splines showing changes or differences as stretches or contractions. The statistics of morphometrics can handle these. Further consideration of anatomical landmarks, however, implies that real biologies are sometimes more complex. Sometimes two-dimensional rubber sheets of anatomies contain cusps or holes representing appearances or disappearances of structures. In three dimensions, equivalent rubber blocks may show not only appearances or disappearances but also reversals of positions of structures. Such phenomena are generally ignored in landmarks and analyses. We show that in some cases morphometrics can take account of such matters. But we also suggest that sometimes these modifications from elastic analogues are so complex that new methods may be required for our morphometric packages. It is in this sense that improvement of morphometrics needs deeper understanding of biology. (shrink)

Several disciplines share an interest in the evolutionary selection pressures that shaped human physical functioning and appearance, psyche, and behavior. The methodologies invoked from the disciplines studying these domains are often based on different rhetorics, and hence may conflict. Progress in one field is thereby hampered from effective transfer to others. Topics at the intersection of anthropometry and psychometry, such as the impact of sexual selection on the hominin face, are a typical example. Since the underlying theory explicitly places facial (...) form in the middle of a causal chain as the mediating variable between biological causes and psychological effects, a particularly convenient conceptual and analytic scenario arises as follows. Modern morphometrics allows analysis of shape both “backwards” and “forwards” . The two computations are commensurate, hence the two kinds of effects can be compared and evaluated as directions in the same morphospace. We suggest translating the morphometric methodology of “Darwinian aesthetics” into this space, where psychological and other processes of interest can be coded commensurately. Such a translation permits researchers to relate the effects of biological processes on form to the perceptions of the same processes in one unified “psychomorphospace.”. (shrink)

Embryos start out as tiny globes, on which many important events occur, including cell divisions, shape changes and changes of neighbors, waves of contraction and expansion, motion of cell sheets, extension of filopodia, shearing of cell connections, and differentiation and morphogenesis of tissues such as skin and brain. I propose to build a robotic microscope that would enable a new way to look at embryos: Google Embryo. This is akin to sending a space probe to Jupiter and its moons, sending (...) back spectacular new visions of their complexity, activity, and beauty. (shrink)

Although Harry Woolf’s great collective volume Quantification mostly overlooked biology, Thomas Kuhn’s chapter there on the role of quantitative measurement within the physical sciences maps quite well onto the forms of reasoning that actually persuade us as biologists 50 years later. Kuhn distinguished between two contexts, that of producing quantitative anomalies and that of resolving them. The implied form of reasoning is actually C. S. Peirce’s abduction or inference to the best explanation: “The surprising fact C is observed; but if (...) A were true, C would be a matter of course; hence there is reason to suspect that A is true.” This article reviews abduction and the Kuhnian dichotomy in a range of classic examples where quantitative reasoning has ended arguments in the natural sciences. Included are John Snow’s discovery of the cause of cholera, Jean Perrin’s proof that atoms exist, the discovery of the double helix, the Alvarezes’ explanation of the extraterrestrial origin of the Cretaceous-Tertiary extinction, and current examples in passive smoking, ulcers, and the anthropogenicity of global warming. Modern biology is a quantitative science to the extent that we operate by “strong inference,” the insistence that our data are surprising on everybody else’s hypotheses but follow as a matter of course from our own, and that we demand numerical consilience whenever we infer across levels of analysis or across disciplines. (shrink)

Bioscientists generate far more data than their minds can handle, and this trend is likely to continue. With the aid of a small set of versatile tools for mathematical modeling and statistical assessment, bioscientists can explore their real-world systems without experiencing data overflow. This article outlines an approach for combining modern high-throughput, low-cost, but non-selective biospectroscopy measurements with soft, multivariate biochemometrics data modeling to overview complex systems, test hypotheses, and making new discoveries. From preliminary, broad hypotheses and goals, many relevant (...) samples are selected and measured with respect to many informative variables. The resulting tables represent a “cacophony” of data. From these, the most relevant and reliable “underlying harmonies and rhythms” are extracted and tested statistically, displayed for interpretation, and used for prediction. Outliers are detected automatically. Interesting subsets of samples can then be chosen for in-depth analyses in subsequent research cycles. This pragmatic, top-down approach takes advantage of developments in both “soft,” data-driven modeling and “hard,” knowledge-driven cultures. Data analytical examples show how information-rich biospectroscopy can be used for characterizing and quantifying known and unknown chemical constituents and physical phenomena in intact biosamples. This is based on a combination of deductive “hard” and inductive “soft” modeling. The examples represent NIR spectra of biochemical mixtures, FTIR spectra of a microbiological fermentation process, and FTIR analysis of fatty acids in milk for functional genomics. (shrink)

The subjectivity or “purpose dependency” of measurement in biology is discussed using examples from high-dimensional medical genetic research. The human observer and study designer tacitly determine the numerical and graphical representation of biological simplicity or complexity via choice of ascertainment , numbers to measure, referential basis, statistical learning formalism and feature search, and also via the selection of display styles for all these quantifications.