Science is a growing system, exhibiting ~4% annual growth in publications and ~1.8% annual growth in the number of references per publication. Combined these trends correspond to a 12-year doubling period in the total supply of references, thereby challenging traditional methods of evaluating scientific production, from researchers to institutions. Against this background, we analyzed a citation network comprised of 837 million references produced by 32.6 million publications over the period 1965-2012, allowing for a temporal analysis of the `attention economy' in science. Unlike previous studies, we analyzed the entire probability distribution of reference ages - the time difference between a citing and cited paper - thereby capturing previously overlooked trends. Over this half-century period we observe a narrowing range of attention - both classic and recent literature are being cited increasingly less, pointing to the important role of socio-technical processes. To better understand the impact of exponential growth on the underlying knowledge network we develop a network-based model, featuring the redirection of scientific attention via publications' reference lists, and validate the model against several empirical benchmarks. We then use the model to test the causal impact of real paradigm shifts, thereby providing guidance for science policy analysis. In particular, we show how perturbations to the growth rate of scientific output affects the reference age distribution and the functionality of the vast science citation network as an aid for the search & retrieval of knowledge. In order to account for the inflation of science, our study points to the need for a systemic overhaul of the counting methods used to evaluate citation impact - especially in the case of evaluating science careers, which can span several decades and thus several doubling periods.