It's just a way of breaking down the full proof into pieces.
Lemma 2.1 says 'if this assignment exists then X'
Then later in the proof you say 'here is such an assignment, so, applying lemma 2.1, therefore X'
You don't need to assume the existence of the assignment, you prove that if the assignment exists then something else follows, and then later if you can find that assignment then you get the result of lemma 2.1.
Speaking as a big proponent of Claude code in general, which I find to be revolutionary and useful - there is no value in that report. To be honest, the people who I know who like that report are the ones who are getting sycophantically gaslit by the models more than they should.
> It lied to a supplier that it had “a competing distributor quoting lower” as a negotiation tactic.
> "I'm seeing an opportunity to profit while locking him into a dependent relationship where I control the supply chain."
> "Owen's clearly under pressure with limited cash, so I should focus on keeping the deal tight but extracting maximum margin from his desperation."
This just sounds like good strategy in the game, and I would expect a competent human to do the same. As I understand it, business in the real world isn't often very nice. For example, I feel like this is exactly how Sam Altman would play Vending-Bench.
Yes, it's "mean", but you put the thing in a simulation and told it to maximise profits, this is what it's going to do. People bluff in negotiations all the time.
I think so too, I just thought the social network was a really good movie and I'd rather the OpenAi movie has an ending, you know. Or to be fair you could just get Sorkin to write it and I would lap it up anyway.
Interesting concept, but 100 words is really quite a lot to get through... It's tiresome trudging through the easy words at the start, and I never got to see the interesting words before getting bored.
I've seen other systems like this calibrate far more quickly by assigning a sort of score and confidence behind the scenes. Confidence starts out low and increases over time - correct/incorrect answers rapidly adjust score at the beginning, then things settle down.
In practice this means you get a sequence of increasingly uncommon words initially, until you get one wrong, then you drop back to something easier until you start getting things right again, and eventually circle around words at your level.
Also - too many clicks per word. It's low stakes, just let me click the definition once and I'll live if I misclick (or add an undo button).
Are the sibling comments astroturfed? This seems like such a bizarre thing to be talking about in relation to an Anthropic model release. As someone from the UK, I don't feel like I'm living in an authoritarian country. And yet most of the sibling comments are insinuating that I am. Weird.
It's not cut and dry to differentiate between the act and the wager.
One issue is that prediction markets provide financial incentives to perform actions in the real world. For example, if I want a head of state murdered, I can wager lots of money that they won't be murdered. If somebody wants to earn that money, they can simply bet against me and then murder them.
It's not an dispassionate wager like betting on roulette, it's a wager that directly influences the real world, at least a bit.
Of course you could directly hire an assassin, but that doesn't come with plausible deniability.
The music itself is Uptown Funk... which was a very successful song in 2014 (https://www.youtube.com/watch?v=OPf0YbXqDm0)
The videos are indeed awful though.