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.
As further evidence of this, Matt cites a fascinating paper from 2019 which looked at the effects of early 20th century prohibition on patents. Turns out that this is a pretty good experiment, because you can examine the impacts of prohibition, as well as compare counties that were already dry (i.e. unaffected by prohibition) against counties that were wet prior to prohibition.
What the study found was that (1) prior to prohibition wet counties were producing more patents per capita (where they bigger and denser?) and (2) wet counties saw a meaningful drop in patents right after prohibition. Previously dry counties went unchanged in terms of innovation.
If you're skeptical of the relationship between bars and innovation, I would encourage you to check out Matt's full post. But know that there is overwhelming research to suggest that new ideas tend to flourish in the big and dense places that we call cities.