This is quite a long post, so it may take some time to write a proper reply, but I’ll get back to you when I can. The focus of this post was on gathering together all the infinite paradoxes that I could manage. I also added some informal thoughts on how surreal numbers could help us conceptualise the solution to these problems, although this wasn’t the main focus (it was just convenient to put them in the same space).
Unfortunately, I haven’t continued the sequence since I’ve been caught up with other things (travel, AI, applying for jobs), but hopefully I’ll write up some new posts soon. I’ve actually become much less optimistic about surreal numbers for philosophical reasons which I’ll write up soon. So my intent is for my next post to examine the definition of infinity and why this makes me less optimistic about this approach. After that, I want to write up a bit more formally how the surreal approach would work, because even though I’m less optimistic about this approach, perhaps someone else will disagree with my pessimism. Further, I think it’s useful to understand how the surreal approach would try to resolve these problems, even if only to provide a solid target for criticism.
This is quite a long post, so it may take some time to write a proper reply, but I’ll get back to you when I can. The focus of this post was on gathering together all the infinite paradoxes that I could manage. I also added some informal thoughts on how surreal numbers could help us conceptualise the solution to these problems, although this wasn’t the main focus (it was just convenient to put them in the same space).
Unfortunately, I haven’t continued the sequence since I’ve been caught up with other things (travel, AI, applying for jobs), but hopefully I’ll write up some new posts soon. I’ve actually become much less optimistic about surreal numbers for philosophical reasons which I’ll write up soon. So my intent is for my next post to examine the definition of infinity and why this makes me less optimistic about this approach. After that, I want to write up a bit more formally how the surreal approach would work, because even though I’m less optimistic about this approach, perhaps someone else will disagree with my pessimism. Further, I think it’s useful to understand how the surreal approach would try to resolve these problems, even if only to provide a solid target for criticism.