I maintain a reading list on Goodreads.
I have a personal website with some blog posts, mostly technical stuff about math research.
I am also on github
Right, that's a good point.
What do you think about "cognitive biases as an edge"?
One story we can tell about the markets and coronavirus is this: It was not hard to come to the conclusion, by mid-to-late February, that a global COVID-19 pandemic was extremely likely, and that it was highly probable it would cause a massive catastrophe in the US. A few people managed to take this evidence seriously enough to trade on it, and made a killing, but the vast majority of the market simply didn't predict this fairly predictable course of events. Why not? Because it didn't feel like the sort of thing that could happen. It was too outlandish, too weird.
If we take this story seriously, it makes sense to look for other things like this - cases where the probability of something is being underestimated - because it seems too weird, because it's too unpleasant to think about, or for some other reason.
For example, metaculus currently estimates something like a 15% chance that Trump loses the election and refuses to concede. I we take that probability seriously, and assume something like that is likely to lead to riots, civil unrest, uncertainty, etc, would it make sense to try and trade on that? On the assumption that this is not priced in, because the possibility of this sort of crisis is not something that the market knows how to take seriously?
I guess this question is really a general question about where you go for information about the market, in a general sense. Is it just reading a lot of "market news" type sites?
Thank you very much!
I guess an argument of this type rules out a lot of reasonable-seeming inference rules - if a computable process can infer "too much" about universal statements from finite bits of evidence, you do this sort of Gödel argument and derive a contradiction.
This makes a lot of sense, now that I think about it.
There is also predictionbook, which seems to be a similar sort of thing.
Of course, there's also metaculus, but that's more of a collaborative prediction aggregator, not so much a personal tool for tracking your own predictions.
If anyone came across this comment in the future - the CFAR Participant Handbook is now online,
which is more or less the answer to this question.
The Terra Ignota sci-fi series by Ada Palmer depicts a future world which is also driven by "slack transportation".
The mechanism, rather than portals, is a super-cheap global network of autonomous flying cars (I think they're supposed to run on nuclear engines? The technical details are not really developed).
It's a pretty interesting series, although it doesn't explore the practical implications so much as the political/sociological ones (and this is hardly the only thing driving the differences between the present world and the depicted future)
I think, rather than "category theory is about paths in graphs", it would be more reasonable to say that category theory is about paths in graphs up to equivalence, and in particular about properties of paths which depend on their relations to other paths (more than on their relationship to the vertices)*. If your problem is most usefully conceptualized as a question about paths (finding the shortest path between two vertices, or counting paths, or something in that genre, you should definitely look to the graph theory literature instead)
* I realize this is totally incomprehensible, and doesn't make the case that there are any interesting problems like this. I'm not trying to argue that category theory is useful, just clarifying that your intuition that it's not useful for problems that look like these examples is right.
As an algebraic abstractologist, let me just say this is an absolutely great post. My comments:
Category theorists don't distinguish between a category with two objects and an edge between them, and a category with two objects and two identified edges between them (the latter object doesn't really even make sense in the usual account). In general, the extra equivalence relation that you have to carry around makes certain things more complicated in this version.
I do tend to agree with you that thinking of categories as objects, edges and an equivalence relation on paths is a more intuitive perspective, but let me defend the traditional presentation. By far the most essential/prototypical examples are the categories of sets and functions, or types and functions. Here, it's more natural to speak of functions from x to y, than to speak of "composable sequences of functions beginning at x and ending at y, up to the equivalence relation which identifies two sequences if they have the same composite".
Again, I absolutely love this post. I am frankly a bit shocked that nobody seems to have written an introduction using this language - I think everyone is too enamored with sets as an example.
This is a reasonable way to resolve the paradox, but note that you're required to fix the max number of people ahead of time - and it can't change as you receive evidence (it must be a maximum across all possible worlds, and evidence just restricts the set of possible worlds). This essentially resolves Pascal's mugging by fixing some large number X and assigning probability 0 to claims about more than X people.