We don't actually have units of 'resources' or optimization power, but I think the idea would be that any non-stupid agent should at least triple its optimization power when you triple its resources, and possibly more. As a general rule, if I have three times as much stuff as I used to have, I can at the very least do what I was already doing but three times simultaneously, and hopefully pool my resources and do something even better.
Machine learning and AI algorithms typically display the opposite of this, i.e. sub-linear scaling. In many cases there are hard mathematical results that show that this cannot be improved to linear, let alone super-linear.
This suggest that if a singularity were to occur, we might be faced with an intelligence implosion rather than explosion.
This is for anyone in the LessWrong community who has made at least some effort to read the sequences and follow along, but is still confused on some point, and is perhaps feeling a bit embarrassed. Here, newbies and not-so-newbies are free to ask very basic but still relevant questions with the understanding that the answers are probably somewhere in the sequences. Similarly, LessWrong tends to presume a rather high threshold for understanding science and technology. Relevant questions in those areas are welcome as well. Anyone who chooses to respond should respectfully guide the questioner to a helpful resource, and questioners should be appropriately grateful. Good faith should be presumed on both sides, unless and until it is shown to be absent. If a questioner is not sure whether a question is relevant, ask it, and also ask if it's relevant.