Statisticians have demonstrated the iriappropriateness of percentage data for petrological purposes except when transformations (e.g., log-ratios) are used to avoid inherent closure. Use of open variables for chemical data (perhaps weight per unit volume, g/100cc) would avoid this problem and permit traditional petrological work to be undertaken. Virtually all compositional data used in petrology are expressed as percentages (e.g., SiO2 wt%, muscovite vol%, Si wt%) or parts per million. Geologists depend on percentage and ppm data for studies of petrogenesis, spatial variability, etc. However, for over four decades, statisticians and mathematical geologists have given dire warnings about the dangers of drawing conclusions from percentage (or ratio) data. In consequence, petrological literature abounds with disclaimers about possible adverse effects that closure constraints (stemming from use of percentage data) may have. The abundant warnings have given little help to geologists for two reasons. First, the precise impact of closure on petrologic analyses and conclusions has been unclear or abstract. Second, a practical and realistic way of avoiding closure in petrology has not been apparent. Problem avoidance might involve either (a) applying statistical or mathematical transformations to standard percentage data to escape the inherent closure constraints that importune petrological conclusions, or (b) using meaningful petrological variables that are free of closure constraints so that traditional thinking and data manipulation can be used without problem. Transformation has been advocated for geological work by Aitchison (e.g., 1982); this approach, which presents considerable geological difficulties, is briefly reviewed here. No attention appears to have been given to the simple approach of using closure-free variables, which is the main subject of this paper. Closed data are compositional data that have a constant sum. Open data can have any value and do not have the constant-sum constraint. Standard rock chemical analyses are closed because the oxides (or elements, etc.), expressed as percentages, sum to 100; in consequence, at least one negative correlation between the variables must exist (Chayes, 1960). The problem of closure is obvious in two-variable systems. In a quartz-feldspar rock, for example, if quartz percentage increases, feldspar must decrease, so there is inherent negative correlation between the components.