>How do you make sure that the LLM doesn't reward hack a proof using these workarounds?
I'm not sure what you mean exactly? There is no soundness issue here, the fact that `sqrt -1` is defined to be 0 does not have any impact on what statements about `sqrt x` can be proved when `x` is positive.
It just means that if you are working on an intermediate step of a proof and you need the result that `sqrt y >= 0` you don't need to provide a proof that `y >= 0`. If you wanted an intermediate result that `(sqrt y) * 2 = y` then you would still need to provide a proof that `y >= 0`, though.
>I suspect there is also some decent optimizations on the backend that make it cheaper and faster for OpenAI to run, and those are the real reasons they want us to use it.
I doubt it, given it is more expensive than the old model.
I assume that they mean that OpenAI will now be obligated to pay a lot of that money back to Disney as some kind of licensing fee. No idea if it's true, but that's the only way his comment makes sense.
It's not ideal, but at least most of these are only used in the `kernel` crate, i.e. if there's a breaking change to these features it should be fixable without widespread changes.
It's possible. It'd just be a 3D visualization and more importantly, stupendously huge. If each cell was a cubic millimeter, the shape would be 3700km wide, and stretch 1/3rd of the way to the moon.
And if each cell was a cubic micrometer (which is a side length 200-300 times smaller than a pixel on a typical screen and 50-100 times thinner than a human hair), it'd still stretch 3.7 kilometers, which is about the length of a commercial airport runway.
That's ok. How could they know that there are companies like Aleph Alpha, Helsing or the famous DeepL. European companies are not that vocal, but that doesn't mean they aren't making progress in the field.
That's such a silly argument. X, OpenAI and others have large Saudi investments. In the grant scheme of things the US is largely indebted to China and Japan.
I honestly think it is.
The amount of people who thinks Europe and EU are the same thing is really concerning.
And no, it's not only americans. I keep hearing this thing from people living in Europe as well (or better, in the EU).
I also very often hear phrases like "Switzerland is not in Europe" to indicate that the country is not part of the European Union.
I think the long term effect will be that photos and videos no longer have any evidentiary value legally or socially, absent a trusted chain of custody.
Yes exactly. And this is kind of already played out with text. The printing press came out, literacy increased. Suddenly anyone could write anything and sign anybody else's name to it. There was a trust crisis. Nowadays, we've just gotten used to it and we look at where text came from instead of just what text says.
For example, I'd rather read a tweet from Paul Graham's account than read a screenshot of a Paul Graham tweet that a stranger emailed to me. In the latter case, the source makes me suspicious, so then I go to a more trusted source, e.g. a reputable news organization, or PG's actually X account.
I'm not sure what you mean exactly? There is no soundness issue here, the fact that `sqrt -1` is defined to be 0 does not have any impact on what statements about `sqrt x` can be proved when `x` is positive.
It just means that if you are working on an intermediate step of a proof and you need the result that `sqrt y >= 0` you don't need to provide a proof that `y >= 0`. If you wanted an intermediate result that `(sqrt y) * 2 = y` then you would still need to provide a proof that `y >= 0`, though.