Today I learned that eye herpes is a thing.
Also, a leading cause of blindness.
Also, that the medicine is $400! I mean, it'd be terrible if something were to happen to that vision of yours...
Also, just to clarify, I wasn't the person to come down with it. Not that there's anything wrong with having herpes.
The correct answer was 1/5 and 1. Thanks for playing everyone!
Anyway, one thing is for sure, the raven paradox is only a paradox because our intuition about the real world leads us away from thinking about the probabilities clearly.
With seemingly endless objects existing in the real world, the tiny amount of new information we get from seeing more non-black non-ravens is negligible, and we usually discard it as a rule of thumb, at least until we get to the point where we have observed all the ravens and implicitly take it into account.
My idea for a puzzle was to calculate the exact probabilities in a toy universe with 5 objects and some number of observations given.
However, I'm not so sure how clear of a question this could be, given the philosophical uncertainty around the question.
Now, the original argument for the raven paradox only talks about seeing black ravens or non-black non-ravens. What about seeing black non-ravens?
I've heard it interpreted as black non-ravens being irrelevant.
However, if we know everything is black then we immediately know all ravens are black too. If we don't know that but observe that black objects are common, then it's less likely that we will see anything non-black. Wouldn't that also increase our confidence in all ravens being black?
If all ravens are black and there aren't any black things, then it stands to reason that you won't find any ravens in a universe devoid of black objects. So, black objects being non-existent or rare means that ravens will be non-existent or rare too.
If you also aren't seeing any ravens (which must be true if you are still seeking the answer, as any counterexample immediately sinks the idea that all ravens are black) then seeing all these non-black non-ravens helps to confirm this situation.
However, non-black non-ravens also add additional evidence. If you have uncovered 4 of the 5 objects, but haven't seen any black objects thus far, you would be somewhat surprised by finding a black object as the last one. This is especially true if the number of objects was larger.
If you had an urn that seemingly had 50% red balls and 50% blue balls and had already taken out 999 of them, then it would be surprising to pull out a black ball as number 1000.
Seeing a black raven adds additional evidence for all ravens being black because it shows that a pattern exists. If the first 4 objects in the universe were black ravens, you would not be surprised by the 5th and final object being another black raven
This is where things get muddy.
The way I understand it, the argument for the raven paradox is just pointing out that non-black objects also add additional evidence. If you see a non-black raven, it immediately disproves that all ravens are black
Uncovering the identity of any of these 5 objects makes it less likely that there are any non-black ravens in this universe, simply because there are fewer opportunities for one to appear (of course, it's always possible that the last object we observe is a white raven). So it's trivial that the core idea of the raven paradox is correct, and seeing something that isn't a black or a raven adds evidence that all ravens are black.
However, that's not what the Raven paradox is actually about.
While thinking up puzzle ideas, I thought of one I can't use for a submittable puzzle, but which I think the Internet would find interesting nonetheless.
The raven paradox says that seeing a non-black non-raven (such as an orange cat) increases the probability that all ravens are black despite this observation being seemingly unrelated.
I think this makes far more sense if you think about a toy universe with just 5 objects in it, rather than the huge real world.
Also, if anyone wants to take this idea for either math/programming puzzles or to do something similar with another topic, be my guest.
Of course, I don't have a staff like Matt Parker seems to have for his puzzles, so it wouldn't be quite the same.
I doubt I could take on the fascinating open problem part for instance, as it sounds like reading emails on the open problem is very labor intensive.
For the involved puzzle, I'm thinking about something in the vein of Matt Parker's Maths Puzzles: https://www.think-maths.co.uk/maths-puzzles
I highly recommend trying out their puzzles.
They're much simpler than something like Project Euler, which requires programming and substantial ingenuity to solve:
However, they're still challenging enough that I usually use programming to assist in solving them. I'm pretty sure they always have a tractable pure math answer though.
It might also be possible to do both types of puzzle. If so, the idea would be to have two different accounts, one for a simple daily (or so) puzzle and one for an involved puzzle on a weekly or biweekly schedule.
The main reason for two accounts is that some people would probably only want to subscribe to one or the other. I could easily see people only interested in the big puzzle becoming annoyed by the fast puzzle.
In the poll, vote for the puzzle type you would expect to enjoy the most.
So, I made a poll that was a math question (with one correct answer).
Would there be interest in taking this concept further, with regular math puzzles being delivered to subscribers as a toot?
If so, would there be more interest in more interesting and involved puzzles less frequently, or simpler but very frequent puzzles?
I'm thinking I could start up a specific account to publish the puzzles, perhaps with a bot to help with administering the puzzles.
One more important technology in the mix is nanotechnology. It's a more fundamental kind of technology, and advances in the field will probably be crucial to the other three fields, but it will probably play a supporting role over the next few decades, rather than being the main driving force.
Java developer by day, Julia developer by night.
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