Seamus Heaney began his translation of Beowulf with "So", rendering the Old English "Hwaet" in a more natural way than the usual archaic "Listen!", "Lo!", "Hark!" kind of thing. In the introductory note, he explains: "'so' operates as an expression that obliterates all previous discourse and narrative, and at the same time functions as an exclamation calling for immediate attention." Far from being a chatty colloquialism, it is a solemn, weighty kind of "so" for Heaney.
Maybe part of the explanation for this specific attack is incompetence - miscommunication, comparatively junior people exceeding their authority, subordinates afraid to object, and everyone doubling down rather than admitting defeat. I could definitely imagine that the people who devised and built out the capability being furious at it being deployed like this.
> BGP announcements, themselves unencrypted, aren't protected with DNSSEC.
This is true, but only because BGP announcements don't involve DNS, and so all the DNS security in the world won't help. Agreed that there is a lot of scope for doing better on BGP security, though - and indeed DNS security.
I wonder if this even needs to be something in the home. Wouldn't it also make sense to install these things, in bulk, in a place where they could service several homes? Say, at the block level. If it is part of power distribution infrastructure as opposed to a consumer product, then that simplifies some of the safety and maintenance issues; concerns like weight or volume are even less important if they are housed in a dedicated structure.
Congratulations! This was the slipperiest of all slippery slope arguments on HN today. Report to the nearest male genocide facility to claim your prize.
The Mill certainly raises a lot of interesting code generation and optimization issues. I'm sure there's plenty of scope for figuring out good optimization strategies, as a lot seems to depend on the ability of the compiler to make good choices about instruction scheduling and belt slot allocation. Sure, that's the case for traditional architectures as well, but there's more prior art there too. There may also be ingenious algorithms which work better on the Mill architecture specifically. I'd love to know if there's any theory on the hardness of allocating positions on the belt, compared to traditional register allocation.
It's interesting, but the problem I have with the presentation is that the modern manifestation of this idea has nothing to do with Buddhism. While we can maybe say that Buddhism came up with some similar-looking stuff, there's no causal link, and the philosophical systems are not working within the same paradigm. Like seeing a human face on the surface of Mars, this is an example of coincidence more than any deep connection.
Well, OK, that's unfair, because Buddhism and formal logic are both human endeavours, and have to deal with the same facts. But this disconnect is even true with parts of Greek philosophy. "Atoms" as we understand them are very different from "atoms" as Aristotle thought of them, even though there is a historical connection. Today's chemists would do badly if they relied on Aristotle for anything other than historical curiosity.
Sperner's Lemma is probably my favorite mathematical result. It is easy to explain, and pretty easy to prove, but it has a higher than average number of "aha" moments along the way. The mathematics is not too intimidating - probably the scariest thing is the generalization to n dimensions, which requires induction. It is also fun to explain the connections to Nash's theorem and so on, as invoked in this article.
This was not a referendum, nor even a proper opinion poll - just a partisan petition. The figure of 89% is completely meaningless. Both the Daily Mail, and this article, prefer to make their own political point (we hate government and taxes) rather than engage in real news reporting or analysis.
I disagree that the slides have to be able to stand alone. Critical material shouldn't be completely ephemeral, but there's no reason that everything has to be on the slides. It can be in lecture notes, textbooks, and so on.
Yes, the interface idea is basically the right thing, but there are technical difficulties which aren't immediately obvious. For example, we'd like to be able to prove that two different implementations of the natural numbers are equivalent (one can do this mathematically, so if our system is going to handle general mathematics then it has to be capable of doing this). So we have to think quite hard about what this "equivalence" actually means. It's not enough to say that they satisfy the same axioms, because in general there can be all kinds of models for some set of axioms. It's closer to say that all number-theoretic statements about numbers-v1 are true of numbers-v2, and vice versa: but you can see that this is starting to get a bit hairy in terms of computable proofs.
A related problem, which speaks to the leaky abstraction issue, is "proof irrelevance". Typically, if I've proved something, it shouldn't matter exactly how I did it. But it turns out to be tricky to make sure that the proof objects in the system don't accidentally carry too much information about where they came from. Sure, you can define a way to erase the details, but you still have to prove that erasing doesn't mess up the deductive system.
None of this is insurmountable, but it's a glimpse into the reasons why encoding mathematics computationally is not trivial.
Right, this is how mathematics really works. But formalizations of mathematics may suffer from leaky abstractions. If we prove facts about numbers by compiling them into sets, and then using set-theoretic axioms, we might accidentally make it possible to prove things about numbers that are incorrect or meaningless.
This is a very good thought. Some current projects are trying to develop computable mathematical foundations in a more structured way. Homotopy type theory (http://homotopytypetheory.org/) is one example that has a lot of buzz around it just now, but automated theorem proving has been trying to work with higher-order concepts for ages now.
In the classical approach of "compiling" everything into sets/logic/etc., you end up with just the assembly language problem that's being discussed, where all the high-level structure vanishes. In order to do your bottom-up approach instead, one of the things that needs to happen is to make the theory really compositional, so that once you've defined some abstraction or higher-level concept, you can use it in constructions and proofs without having to break the abstraction. You don't need to know - and in fact you shouldn't be able to find out - just how the natural numbers were constructed, as long as they work by the right rules. This motivates the use of type theory to describe mathematical objects, and say which operations are allowed. We want to be able to add two numbers and get another number, but we don't want to be able to intersect two numbers as if they were sets, even if they happen to have been built out of sets.
So I think you are right - or at least, there are plenty of people who agree with you that this is a good idea. It is difficult to actually do, of course, but that's life.