Understanding is a poor substitute for convexity (2012)

This is an extremely flawed initial assumption. There is no requirement for chance to be centered around zero. Consider rolling a dice: sometimes you'll get more than the mean, sometimes less, but you'll never roll a negative number. You can certainly win on chance in the long run, that's the foundation of casinos and insurance companies. It's hard to imagine a scenario where trial and error can possibly lead to knowledge regressing.

Consider randomly digging holes in the ground: after enough holes you will eventually strike gold, and you will never lose physical gold in the process. However, you may lose significant time, wealth, and effort that could have been better converted to gold. The optimal way to strike gold is not to dig more, shallower holes, but to learn enough geology to understand where gold is likely to be found and concentrate your prospecting there.

No experiment could ever possibly hurt scientific knowledge. People tinkering will certainly make occasional discoveries. In a brand new field with a lot of low hanging fruit, these discoveries will be numerous and the cost will be low. But in a developed field where people have a good idea where the remaining discoveries are likely to be found and the effort to conduct such experiments is substantial, targeted approaches become optimal. Reducing the unit cost of experiments is always nice, but is not generally feasible. This strategy of "convexity" is a very poor substitute in the real world for understanding.

If this was modified to “chance alone” then it might be correct. The way it’s worded now makes it sound like chance cannot contribute to long term gains, which is clearly false. Evolution depends on chance (generation of diversity) followed by a selection process and clearly that works pretty well.

I don't know enough about geology to be able to comment intelligently on your digging holes in the ground point. However, from my own background in biology research, a lot of what he writes strikes true with some caveats.

Biological systems are highly complex, and a lot of reductionist basic research work does seem to be driven by understanding along the forms of "I have a mental model of this subsystem, if I do X, then I expect Y." However, a lot is also discovered via his "convexity" principles (which I agree most laypeople would label as "trial and error"). Biologists often discover functions by randomly mutating billions or trillions of individual microbes, screening for interesting phenotypes, and then sequencing to discover the supposedly causal mutations.

Where the understanding approach really breaks down is in engineering systems -- which I believe requires an even higher level of understanding than the qualitative mental models bandied about in biology. We simply don't understand enough to be able to develop most drugs with that sort of rational approach, so reducing costs per attempt (while keeping all else equal, which is something often overlooked) would be beneficial. Unfortunately, things in the industry appear to be heading the other direction.

Maybe The Great Leap Forward when Mao killed a bunch of intellectuals?

In simple terms, he's just saying that it needs to be safe to take chances in order for it to be worthwhile to take chances. As you say, science is an example of a system where it's often safe to take chances, because you don't risk losing any knowledge from a failed experiment. (But that doesn't mean there are no costs! You can lose time and money. And I'll also point out that some experiments can be dangerous.)

In any search, whether you can find something interesting is going to depend at least partly on the landscape, so understanding the landscape better will improve the search process, along with your estimates of whether it's worth doing at all. Calling this property of a desirable landscape "convexity" doesn't, in itself, help you understand the landscape, but it doesn't seem wrong?