3,851 karma · joined April 14, 2013
Do I fully believe all of the above? Not exactly. But compiler authors do. Does it make a really good argument to never use C or C++? Yes. If only we had 50 years of optimization work in any language with better semantics.
To be clear, Google was doing this out of self-interest. Paying user ISPs for access to those users is not a cost they want to pay. But it's the same as any other protection racket. A local shopkeeper has personal reasons to not want to pay off the mob, but that doesn't mean their position is wrong.
But yeah; don't join the military.
Try checking in only your prompts and nothing else. Just the parts you actually typed. See how well it works to regenerate the same application next week, let alone next year. Prompts are fundamentally a different sort of thing from code. Do not mix them up.
Assembly makes non-local reasoning mandatory, as any code can update any location in memory without restriction. All memory accesses are global. References need not even be by name - they can be via computed addresses. There are no restrictions in place allowing the structure of the program to provide boundaries on what pieces of code may be understood as units.
This isn't some slapdash random patching. Everyone involved knows that assuming that the λ in λCDM is a constant is shaky. It could be a function of time, or even location in some way. But it's simplest if it's a constant. So you start by modeling the universe as if it is. Then you determine what sorts of observations would support or contradict that, and you start making them. When you get results, you start examining what version of the model best explains those observations. And someone somewhere goes off to try find a better model than any version of λCDM. If they succeed, their model will eventually supplant it. This is how science progresses, even if the experiments are less under the control of the experimentors than they'd like. The important part that you make revisions in response to observations.
(FWIW, particle physicists are constantly frustrated that they can't find counterexamples to the Standard Model. They know it has to be incomplete, but the lack of contradictory observation leaves them no direction to try to improve it.)
I honestly am curious. I've seen a few examples presented for it, but they always seem like bad software engineering to me. Where's an example that does something in a cleaner way than alternatives present in other languages while remaining compatible with local reasoning?
I don't think raw machine code (not even assembly) is the best form to reason about program logic. It just takes too many steps to execute sophisticated processes to keep them all in your head at once - or keep them all in an LLM context at once.
Truth is some sort of value judgment that is outside the scope of formal systems. And looking at how bizarre Gödel statements are, it's unclear if there's any particular justification for declaring them to be true or false.
I've done both of those things. I know what you get taught. But I've kept my math education going for the 25 years since then. I've talked to practicing mathematicians about what they do. I've learned a lot about the scope of math.
As an aside: most people really dislike it when I say that they should be much more precise about different numerical systems. The integers are not a subset of the rationals. They are entirely different constructions, but there is an isomorphism between integers and a subset of the rationals that preserves the integers' ring structure within that subset of the rationals and a few other aesthetic concerns. You can see why no one wants to communicate like this, even if they acknowledge it's technically correct. So I know all about pushing symbols around.
But I also know that pushing symbols around isn't the whole story. Pushing symbols around is only useful as a final check. Do you want to validate that 1+2=3? Pushing symbols around can help. But how do you decide that the ideas behind 1, 2, 3, +, and = are worth having precise and compact representations?
Math doesn't just use formal systems to generate proofs. It's not enough for symbols to be arranged neatly according to some rules. Math is also the process of creating the sets of symbols and their rules and communicating to other people why this set of rules and symbols is interesting. What ideas get preserved when you are working with this system? What is it an abstraction over?
But mathematics is not a collection of facts. Mathematics is the study of abstraction. And what do you learn from a single data point? What can you abstract from that?
That's why just being a counterexample isn't really interesting. There has to be more than "counterexample" for there to be something to abstract. Was it generated from an analysis of the problem? Can the counterexample be generalized to explore the problem further? Is the counterexample a surprise in a way that suggests something is missing from current understanding?
Being a counterexample doesn't mean that something isn't interesting to a mathematician. But it's also not the interesting part.
The danger isn't everyone but you getting wealthy. The danger is that wealth tends towards concentration. And it tends to concentrate around people who are already wealthy. The danger is, bluntly, that things will get worse for all but a few and most people will be so caught up in a red queen's race that they can't see how to stop.