One of the reasons why I remain so bullish on cities is because we know that new ideas disproportionately come from cities (typically big and dense ones). Matt Clancy does an excellent job of explaining this in a recent post. In it, he cites a number of studies that suggest density is pretty good. It's good for not only increasing innovation, but also for increasing the diversity of innovation.
One of the studies found that, all else being equal, doubling the number of jobs per square mile resulted in 20% more patents per capita. Matt argues that the reason for this is that density allows us to meet and collaborate with new people. With this is mind, what do you think that working from home (which is the opposite of job density) might do to innovation/patents?
Another one of the studies that Matt cites in his article deals with the correlation between patents and street grids. Denser street networks seem to have a marginally positive relationship with innovation.
But Matt surmises that this may not be because it means we're all serendipitously bumping into each other all over the place; instead a denser street network is likely symptomatic of other things -- namely an increase in "third places." Because if you consider which census blocks have a concentration of restaurants, cafes, and bars, the number of patents then goes up meaningfully.