svat

Both "search" and "everything else" are primarily advertising revenue[1], and advertising spend is always heavier in Q4 because of (Black Friday and) Christmas.

[1]: As the page says,

- "Search" means "ads on Google Search and on other Google properties such as Gmail, Maps and Google Play"

- "Everything else" means "YouTube ads, subscriptions and devices, Google Network and Other Bets".

I should add a clarification about the phrase “understanding what is in it” in the previous comment, which I realized is ambiguous: obviously, if you care to distinguish what is present vs absent in a paper, you need to read it. But if you care about understanding any new mathematical content it may have (as applies to this case, as I've been saying in this entire thread — if you, like Prof. Harvey care about a potential o(n log n) algorithm, whether or not such an algorithm is contained in OpenAI's paper per se), then it is neither necessary nor (given how it's written) a good idea.

As I said in the linked comment, it does not matter whether the idea came from OpenAI's paper, or was hallucinated by Fable, or was arrived at by the reader while reading a potential nonsensical explanation from Fable: the main message is that the “o(n log n) bound is plausible” and it is valuable to have it come from a human expert.

I looked into it, and it seems there are two issues:

- Only a (growing) minority (maybe 15%?) of apps on F-Droid (the "reproducible builds" ones?) are signed with the developer's own keys (rather than being signed by F-Droid), so to avoid the user having to do the 24-hour cooldown, the developer of the app would need to have done developer verification and signed the app with their own keys,

- F-Droid is in principle opposed to developer verification so the F-Droid client itself would probably not count as by a verified developer.

So in principle a user could avoid the 24-hour cooldown by installing the F-Droid client using adb, then installing from F-Droid only the apps signed by developers who have gone through the developer verification flow, but in practice I imagine most of us (as users) will be doing the "Advanced" flow, i.e. the one-time 24-hour cooldown.

That's fair; there is some slight evidence in the linked comments of pressure from those governments, but you're right, Google's own comments show it agreeing with the principle. E.g. they say that identifying and banning malicious apps isn't very effective if the developers can make slight changes and distribute modified apps immediately. So the basic idea of anonymous apps having wide distribution is what is being targeted.

Come on. Prof David Harvey is the leading expert on this exact topic (integer multiplication algorithms), and here he has spent a lot of effort and time to digest the main new idea(s), and write 30+ pages explaining exactly what he's understood and why he believes the result is plausible. About the main “gadget”, he writes “I have worked through all the steps pretty carefully, and I think it checks out.” All this is useful information, and is the best we have so far from a reliable human source. I think it deserves more than a flippant response to the first line.

- The author is already the world's best expert on this topic.

- You're right that it's possible Fable came up with a different o(n log n) algorithm that is not in OpenAI's paper, but (apart from being unlikely) it doesn't matter, as he talks of the belief that “the main result is possibly correct”, not necessarily that OpenAI's paper is: whether the argument comes from the paper or from Fable, the question of interest is whether multiplication is really possible in o(n log n) time. The point is that there's a genuine idea here, somewhere between OpenAI's paper and Fable's explanation of it and the author's understanding of it.

- This is in fact how mathematicians have evaluated papers for decades: is there any way this result could be true? Is there an actual idea here that could help? Do I understand enough of the argument to be convinced it's likely true, modulo some details that need to be filled in? The last step (actually filling in the details) happens when teaching it to someone else or writing it again in one's own words.

The very next lines say:

> At first I did not understand Fable’s explanations. But I asked questions, and then asked more questions, and drilled down towards the core of the problem. Gradually I started to understand parts of the argument. I have seen enough now to arrive at the tentative belief that the main result is possibly correct […] In the sections below I will try to explain what I have learned so far, and why I lean towards thinking it might be correct.

So the whole paper is about things the author does understand. (BTW the author David Harvey was behind the big advances in integer multiplication, in 2014 and 2019/2021.)

Every community approaches problems with the tools at its disposal. Doing mathematics is about thinking, so mathematicians approach problems (at least in public) with more thinking and less emotion (than some fields where emotion is much more important). While you and I may appreciate this approach (and even be inspired by it), it remains to be seen whether it ultimately makes the outcomes any better.