We put asterisks next to proofs that use the axiom of choice. If a machine comes up with proof that’s not verifiable by humans, you can very well be sure that there will be asterisks.
+1 The worst code I had to maintain was code that tried to follow DRY (without the trying to understand what the original intention of that principle was). The only way out of that mess was widespread code duplication.
I would argue that out makes even more sense in the era of LLMs. LLM shaped tasks are tasks that we would hand out to junior engineers. Now, I can implement one of these tasks in 1hr instead of waiting for a junior engineer to finish this in 1-3 days. This means the equation for investing in junior engineers has shifted towards disfavoring investment.
Moving running computers around and maintaining connection would have required large trucks and very long cables at the time the internet was invented.
> If a project in an unsafe language has ever had a memory bug (I'm looking at you, Bun), the maintainers objectively have a track record of not being capable of manual memory management. You wouldn't put a person who has a track record of crashing busses at the wheel of a school bus.
I am sure they have this. What tends to happen is that the gradual rollout system becomes too slow for some rare, low latency rollout requirements, so a config system is introduced that fulfills the requirements. For example, let’s say you have a gradual rollout for binaries (slow) and configuration (fast). Over time, the fast rollout of the configuration system will cause outages, so it’s slowed down. Then a requirement pops up for which the config system is too slow and someone identifies a global system with no gradual rollout (e.g. a database) to be used as the solution. That solution will be compliant with all the processes that have been introduced to the letter, because so far nobody has thought of using a single database row for global configuration yet. Add new processes whenever this happens and at some point everything will be too slow and taking on more risk becomes necessary to stay competitive. So processes are adjusted. Repeat forever.
Maybe it helps to think of matrix multiplication as a special case of the composition of linear transformation. In the finite dimensional case they can be expressed as matrix multiplications.
Bismarck was afraid of workers unionizing and transformed a working healthcare system owned by workers into a state owned one. That move significantly reduced the utility of worker unions, which was the goal behind it.
I don’t think it’s a wordplay with the r-word, but rather a reference to the famous Shakespeare quote: “Hoist with his own petard”. It’s become an English proverb. (A petard is a smallish bomb)
I actually used the examples from that paper for testing. The results that they are showing in the paper are different from mine and I think that git changed as well. I believe the conclusions from that paper no longer hold.
One use case where I never want to miss it is in tests: Understanding what the differences between the expectation and the actual result are is invaluable.
A minimal diff is one where the number of edits is minimal. The context around edited lines does not count as edits, because they are matching lines. That said, minimal is definitely only a proxy, that’s why is a good property to relax.
> Even if something does align better with real numbers, it's still just x+0i
Beware, it’s not always useful to work in complex numbers, you sometimes want to do something different for reals and complex numbers. The prime example here is complex analysis. Defining differentiation is based on limits, on the complex plane there are a lot more directions to approach a limit vs just two on the real line. This has some interesting implications. For example, any function differentiable on the complex plane is infinitely differentiable.
> The equal sign should be reserved for comparisons, because that is what it means in mathematics.
This is touching on a pet peeve of mine: Mathematics and programming are similar in many aspects, but this is not one of them. In mathematics = is not a comparison, but a statement.
More generally, mathematics is about tautologies, that is statements that are always true. In programming, a comparison is evaluated to either true or false.
That doesn’t mean that there’s no room for conditionals in mathematics (one example is piecewise function definitions). But it’s not the same. Heck, even the definition of “function” is different between mathematics and programming.