2. That the worst-case is very hard usually tells you that many instances will be hard (unless you discover an easy subclass), as is the case here. And when many "natural" instances are easy, that means that the problem is more interesting than perhaps previously thought, and it requires and receives more research, not less. If most instances are near the worst case, it means you know all there is to know about the problem; when they're not, it means there's more to study.
A program that enumerates all theorems in ZFC and stops when it proves a contradiction (e.g. true = false). Encoding a program that is equivalent to that directly as a Turing Machine in merely 748 states: https://www.scottaaronson.com/papers/bb.pdf (meaning that we cannot prove an upper bound on the 748th Busy-Beaver number, but there are probably even smaller undecidable TMs).
But my favourite example (shown here in Java) demonstrates the difficulty of analysing simple, realistic programs without necessarily being undecidable:
long foo(long x) {
if (x <= 2 || (x & 1) != 0)
return 0;
for (var i = x; i > 0; i--)
if (bar(i) && bar(x - i))
return i;
throw new Error();
}
boolean bar(long x) {
for (var i = x - 1; i >= 2; i--)
for (var s = x; s >= 0; s -= i)
if (s == 0)
return false;
return true;
}
Even in this case where even the input space is finite (and so everything here is definitely decidable), we simply don't yet know whether there is some x for which foo(x) throws, let alone if we made the input unbounded by using BigInteger instead of long.
> Given that the phrase “adjust the imports”—again, in a statutory
provision that did not use specific words such as “tariff ” or
“duty”—was unanimously held by this Court in 1976 to
include tariffs, and given that President Nixon had
similarly relied on his statutory authority to “regulate . . .
importation” to impose 10 percent tariffs on virtually all
imports from all countries, could a rational citizen or
Member of Congress in 1977 have understood “regulate . . .
importation” in IEEPA not to encompass tariffs? I think
not. Any citizens or Members of Congress in 1977 who
somehow thought that the “regulate . . . importation”
language in IEEPA excluded tariffs would have had their
heads in the sand.
The roll-call vote for HB7738 (IEEPA) was not recorded [2], so we seemly can't confirm today how any sitting members voted at the time. But there are two members of Congress remaining today who were present for the original vote: Chuck Grassley (R-Iowa) and Ed Markey (D-Mass). They clearly both agree with the Court, while having different opinions on the tariffs themselves.
Statement by Grassley [3]:
> I’m one of the only sitting members of Congress who was in office during IEEPA’s passage. Since then, I’ve made clear Congress needs to reassert its constitutional role over commerce, which is why I introduced prospective legislation that would give Congress a say when tariffs are levied in the future. ... I appreciate the work [President Trump] and his administration are doing to restore fair, reciprocal trade agreements. I urge the Trump administration to keep negotiating, while also working with Congress to secure longer-term enforcement measures.
Statement by Markey after previous decision in August [4]:
> Today’s ruling in the U.S. Court of Appeals for the Federal Circuit makes it clear that President Trump’s chaotic tariff policy is illegal. ... Today’s ruling is an important step in ending the economic whiplash caused by Trump’s abusive tariff authority.
N=2 is scant evidence, but it seems like both sides of the aisle "had their head in the sand", or Justice Kavanaugh's historical interpretation is a bit off.
I’m no industry insider, but tipping would seem to me to be a key indicator for discretionary spending, so a very valuable data point. I have no doubt that a dataset of 1m clients and their tipping patterns would be worth >500k per client (dataset user). A list of consistent, large or skimpy tippers significantly more. (Skimpy so as to know to target them with “deals”, big tippers for the upsell and value added advertising.
E.g. Uber / UberEats offer lower fairs to drivers if the client is expected to tip higher. I'm not an insider, but it can be observed in the wild as discussed on Reddit.
In my research I take notes exactly as described here. I use plain-text files, one per week, with dated sections using markdown-ish notation where convenient. Display is never a goal; approximately 80-char column plaintext is the target format.
I agree with other commenters here that typing gives me more flexibility, in particular when writing arguments. I’ll format each point as a bullet and rearrange the list until I’m satisfied with the flow.
The notebook is essential for recovering tidbits learned along the way, e.g. what tricky steps did I need to get that one dependency to build. Weekly notepads are coarse enough to search by memory and contain enough context to get oriented quickly when going back several months.
I recall a paper from many years ago (early 2010s) describing methods to estimate the camera motion and remove motion blur from blurry image contents only. I think they used a quality metric on the resulting “unblurred” image as a loss function for learning the effective motion estimate. This was before deep learning took off; certainly today’s image models could do much better at assessing the quality of the unblurred image than a hand-crafted metric.
This is... hard to follow. You seem to be implying that Cloudflare is covering for USG's failed military op-sec surrounding a malicious BGP leak, and judging that this is such a bad action (on the part of Cloudflare) to undermine your trust, not only in Cloudflare, but in all companies and the US government entirely. I don't think the situation is so dire.
Cloudflare's post boils down to Hanlon's razor: a plausible benign interpretation of the facts is available, so we should give some scrutiny to accusations of malice.
Are there specific relevant facts being omitted in the article, or other factors that diminish Cloudflare's credibility? They're clearly a qualified expert in this space.
Let's assume for the sake of argument that the BGP leaks (all of them from the month of December, in fact) were the result of secret US military intelligence operations. The fact that militaries generally use cyber vulnerabilities to achieve their objectives is not news, and the US military is no exception. Keeping specific exploits secret preserves a valuable advantage over competitor states.
One could argue that Cloudflare's post helps to preserve USG's secrecy. We can't know publicly whether USG solicited the article. But even if we assume so (again assuming malice): Is Cloudflare wrong to oblige? I don't think so, but reasonable people could disagree.
Merely pointing out Hanlon's razor doesn't fundamentally change the facts of the situation. In Cloudflare's expert opinion, the facts don't necessarily implicate USG in the BGP leaks without an assumption of malice. Assuming Cloudflare is malicious without justification is just deeper belief in the conspiracy that they're arguing against.
If Cloudflare is distorting the facts, we should believe (rightly) that they're malicious. But I don't see any evidence of it.
