The history of science is much more variegated than assumed in the Edge Question about the abandonment and burial of old ideas. While the view that new ideas triumph by replacing old ones fits some scientific developments, in many other cases new ideas take over a vacuum formerly occupied by no well-articulated idea at all. That happens for either of two reasons: new ideas responding to new information made possible by new measurements, or else responding to new "outlooks." (Among historians of science, the term used rather than the inadequate English term "outlook" is the German word Fragestellung –literally, the posing of a question, but more broadly meaning a world view from which that question can arise). I'll give two or three examples illustrating each of those two reasons.
The most familiar modern example of a new idea made possible by new measurements is Watson's and Crick's double helix model of DNA's structure. Their model didn't replace a previous established model whose opponents gradually died out without abandoning their error. Instead, the model was made possible by two recent sets of measurements: analyses of the chemical composition of DNA (revealing equivalent amounts of the bases adenine and thymine, and of cytosine and guanine); and X-ray crystallographic evidence. As is well known, two models of DNA structure were then proposed nearly simultaneously, by Pauling and by Watson and Crick. It almost immediately became obvious that the former model was wrong, and that the latter model did account for all of the evidence. Hence the Watson and Crick model became rapidly accepted, replacing a vacuum rather than a previous wrong theory.
My other example of an idea made possible by new measurements concerns the origins of animal electricity. Our nerve and muscle membranes operate by conducting electrical impulses, arising from a change in transmembrane voltage between active and inactive membrane regions. In the absence of direct measurements of transmembrane voltage, it was impossible to propose a quantitative theory for how that voltage could change. That problem was solved between 1939 and 1952 by two developments: the anatomist J.Z. Young discovered giant nerves in squid, and physiologists developed microelectrodes small enough to insert into squid giant nerves without damaging them. Between 1945 and 1952 the physiologists Alan Hodgkin and Andrew Huxley took advantage of that anatomical discovery and that technical development to measure the electric currents moving across squid nerve as a combined function of voltage and time, and thereby to reconstruct quantitatively and in detail how a nerve impulse arises from changes in nerve membrane permeability to the positively charged ions sodium and potassium. The Hodgkin-Huxley theory was rapidly accepted because it was so convincingly correct, and because it had no serious competitors. When I was a physiology student in the 1950's and 1960's, the only resistance to the theory that I recall involved some concern by non-physiologists about whether microelectrodes were causing damage to nerve membranes (a concern answered by several types of control experiments), and a non-quantitative proposal that nerve membranes and synapse or junction membranes undergo the same permeability changes (it turned out that they don't).
As for new ideas made possible by a new Fragestellung, consider first the foundation of the several modern sciences constituting population biology: i.e., taxonomy/systematics, evolutionary biology, biogeography, ecology, animal behavior, and genetics. At least until recently, most research in all of those fields except genetics involved observations, counting, and measurements requiring no equipment. Most of that research could have been done by Aristotle, Herodotus, and their contemporaries in classical-age Greece over 2000 years earlier. The Greeks were eminently capable of patient, accurate, quantitative observations of planets and other features of the natural world. Aristotle could similarly have examined Greek animals and plants and arrived at Linnaeus's hierarchical taxonomy; Herodotus could have compared the species of the Black Sea with those of Egypt and thereby founded biogeography; and any ancient Greek could have grown and counted pea varieties as did Gregor Mendel in the 1860's, noticed the differences between Willow Warblers and Chiffchaffs (a related warbler species) as did Gilbert White in 1789, watched young geese as did Konrad Lorenz after 1935, and thereby founded genetics, ecology, and animal behavior. But ancient Greeks lacked the necessary Fragestellung that lent interest to counting pea varieties and scrutinizing warblers and young geese. The rise of those branches of population biology from the 1700's onwards was due to a modern Fragestellung that generated data (without the need for invention of microelectrodes or X-ray crystallography), which in turn generated ideas, in areas where previously there had been neither data nor detailed ideas.
Without going into specifics, I'll mention two other examples of important broad fields that arose only in recent centuries without any need for specialized technology, and that the ancients could have developed but didn't because they lacked a relevant Fragestellung. The Greeks and Romans were in contact with speakers of Indo-European and Semitic and other languages, could have discovered the groupings of languages in those language families, and could thereby have developed the ideas of historical linguistics—but they didn't even bother to record words of their Egyptian, Gaulish, and other subjects. In all of classical Greek and Roman literature I am not aware of a single wordlist recorded for any "barbarian" language, in contrast to the wordlists that European travelers began routinely to gather among non-European peoples from the 1600's onwards. The Greeks and Romans could equally well have noticed the observational evidence used by Freud to explore the unconscious within us—but they didn't.
All of this is not to say that the view underlying this year's Edge Question is always wrong. Examples in the fields in which I work myself include: the replacement of biogeographic theories assuming a static Earth by the acceptance of continental drift, from the 1960's onwards; the rise of the taxonomic approach turned cladistics at the expense of previous taxonomic approaches, also from the 1960's onwards; and the rise in the 1960's and 1970's, followed by the virtual disappearance, of attempts to make use of irreversible (non-equilibrium) thermodynamics in the fields of population biology and of cell physiology. Instead, my main point is that the development of science follows much more diverse courses than only or predominantly the course of abandoning old ideas.