If the color of the number is considered to be an intrinsic property of the number, then under the Bruce Framework, yes, |C|<|B| and |C|=|A| and |B|=|A|.
So then because the winner alternates at an even rate between the two sets, you can intuitionally guess that they are equal?
I like this a lot! I'm curious, though, in your head, what are you doing when you're considering an "infinite extent of "? My guess is that you're actually doing something like the "markers" idea (though I could be wrong), where you're inherently matching the extent of on A to the extent of on B for smaller-than-infinity numbers, and then generalizing those results.
For example, when thinking through your example of alternating pairs, I'm checking to see when =3, that's basically containing the 2 and everything lower, so ...
Yep, absolutely! It was actually through explaining Hilbert's Hotel that Bruce helped me come up with the Bruce Framework.
I do think it is odd though that the mathematical notion of cardinality doesn't solve the Thanos Problem, and I'm worried that AI systems that understand math practically well but not theoretically well will consider the loss of half an infinite set to be no loss at all, similar to how if you understand Hilbert's you'll believe that adding twice the number of hotels is never an issue.
I'm posting this here because I find that I don't get the feedback or discussion that I want in order to improve my ideas on Medium. So I hope that people leave comments here so we can discuss this further.
Personally, I've come across two other models of how humans intuitively compare infinities.
One of them is that humans use a notion of "density". For example, positive multiples of three (3, 6, 9, 12, etc.) seem like a smaller set than all positive numbers (1, 2, 3, etc.). You could use the Bruce Framework here, but I think that what we're actually doing ...
To (rather gruesomely) link this back to the dog analogy, RL is more like asking 100 dogs to sit, breeding the dogs which do sit and killing those which don't. Overtime, you will have a dog that can sit on command. No dog ever gets given a biscuit.
The phrasing I find most clear is this: Reinforcement learning should be viewed through the lens of selection, not the lens of incentivisation.
I was talking through this with an AGI Safety group today, and while I think the selection lens is helpful and helps illustrate your point, I don't think the analogy...
When you say "the dog metaphor" do you mean the original one with the biscuit, or the later one with the killing and breeding?
It is! You (and others who agree with this) might be interested in this competition (https://futureoflife.org/project/worldbuilding-competition/) which aims to create more positive stories of AI, which may help shift pop culture in a positive direction.
I had a friend in a class today where you need to know the programming language C in order to do the class. But now with ChatGPT available, I told them it probably wasn't that big of an issue, as you could probably have ChatGPT teach you C as you go through the class. I probably would have told them they should drop the class just one semester ago (before ChatGPT).
My personal analogy has been that these chat bots are like a structural speed up for humans in a similar way that Google Docs and Drive were for working on documents and files with people - it's ...
Small typo in point (-2): "Less than fifty percent change" --> "Less than 50 percent chance"
I say this because I think it relates to / could be within your same world:
One of my favorite current story ideas is to write a story where there's a girl who lives in a world where each society is running an experiment about the best way to live life. In school, she finds out that while most societies are aware of the experiment that's being run, her society is one of the few where the experiment is kept secret from the people in it.
As she grows up, she realizes how poor her society is, and how little technology they have. It improves very quickly over th...
I have not read through this in its entirety, but it strikes me that an article I wrote about how the mathematical definition of infinity doesn't match human intuitions might be useful for people to read who are also interested in this material. I'm also fairly new here, so if cross posting this isn't okay, please let me know.
https://london-lowmanstone.medium.com/comparing-infinities-e4a3d66c2b07
Is it possible to hide the values of other predictors? I'm worried that seeing the values that others predict might influence future predictions in a way that's not helpful for feedback or accurate group predictions. (Especially since names are shown and humans tend to respect others' opinions.)
Yeah, that sounds right! I think this video supports that idea as well:
For example, when asked to think about something I would like more deeper, masterful knowledge about, I replied "artificial neural networks".
The closest thing I could think to potentially experiencing them and interacting is either 1. Through interactive demos or 2. Through a suit like this. I'm unsure if that is what is meant by interaction, though it does seem closer.
This is my first comment on this site, so if I'm missing particular norms, please let me know.
I understand why this was done, but it is amusing to me that in order to describe what "contact with the territory" looks like, you must use map-like terms such as "arm", "finger", and "hand".
I was going to recommend that you could qualify all of these terms, but I realized that this would likely not be needed for most readers; hopefully most people will understand, after having reading the previous essays, that by "hand", you're taking advantage of our prec...
it sounds like you understand a core component of why this sequence was so bloody difficult to write.
I agree. It also would be very odd if there was a high increase overall that that the paper would not directly state that as their main finding. Instead, the paper's main claim is that sports betting "amplifies" emotions and impacts on domestic violence.
As you point out, if there's an unexpected loss, the domestic violence rate increases more in places with gambling, but, on the other hand, if there's an expected win, the domestic violence rate decreases more in places with gambling.